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## Inequalities Worksheets

Teeming with adequate practice our printable inequalities worksheets come with a host of learning takeaways like completing inequality statements, graphing inequalities on a number line, constructing inequality statements from the graph, solving different types of inequalities, graphing the solutions using appropriate rules and much more for students in grade 6 through high school. Solutions to inequalities are infinite and are presented as an interval. Kick-start practice with our free inequalities worksheets!

» Translating Inequality Phrases

» Compound Inequalities

» One Step Inequalities

» Graphing Linear Inequalities

» Two Step Inequalities

» Absolute Value Inequalities

» Multi Step Inequalities

» Quadratic Inequalities

Completing Inequality Statements

Tackle this batch of printable inequalities worksheets by plugging each of the four options in the inequality statement. Grade 6 students circle all the possible values that make the inequality statement true.

Graphing Inequalities on a Number Line

Graph the inequality on a number line by drawing a circle over the number. Fill it if the inequality has a ≥ or ≤, leave it unfilled if it has a > or <. Draw a line toward the right, if the solutions are greater than the number and toward the left if they are less.

Writing Inequalities from Number Lines

Study the graph, and construct the inequality that best describes it. Grade 7 students look for open and closed circles, watch for the direction of the line and build an inclusive or strict greater than or less than inequality in no time.

Identifying the Solution Graph

If buffing up skills in solving and graphing inequalities is on your mind, then these printable inequalities worksheets should be your obvious choice. Students choose the graph that best describes the solution for each single variable inequality.

Identifying Inequalities from Number Lines

Observe the graph in these pdfs keenly and construct an inclusive inequality with a closed circle or a strict one with an open circle. Students in 7th grade and 8th grade use < if the line extends toward the right and > for a line stretching toward the left.

Identifying Solutions in Interval Notations

Draw logical conclusions, whether the interval with a bracket or parentheses is the right solution to the inequality. The task in these pdfs for grade 8 and high school students is to choose the correct interval notation that best describes each inequality.

Translating Inequality Phrases Worksheets

Primarily focusing on reading phrases and converting them into algebraic inequalities, these printable worksheets are sure to give students an insight into comprehending inequalities and their real-life connection.

(12 Worksheets)

One Step Inequalities Worksheets

Are you looking for a variety of exercises to introduce or recapitulate one-step inequalities? Then be assured you are in the right place. With a host of pdfs for your 6th grade students to choose from, there'll be no dearth of practice material.

(51 Worksheets)

Two Step Inequalities Worksheets

Refine your skills in solving and graphing inequalities in two simple steps. Grade 7 students separate the like terms on either side of the inequality. Use inverse operations to isolate the variable and solving the inequality will be duck soup.

Multi Step Inequalities Worksheets

Work methodically toward solving and graphing the multi-step inequalities. With the adequate practice provided in these worksheets finding solutions to multi-step inequalities will no longer be a hard nut to crack for your students in grade 8.

(45 Worksheets)

Compound Inequalities Worksheets

Whether you are looking for inequalities that are joined together by the conjunction "and" or "or", these worksheets on inequalities beef up practice and prepare high school students in solving and graphing such inequalities.

Graphing Linear Inequalities Worksheets

Visualize the inequality on a graph, analyze the properties of the line, observe the graph and figure out the inequality, sketch the inequality graph are some exercises present here to challenge your high school students.

(24 Worksheets)

Absolute Value Inequalities Worksheets

What happens when two important concepts absolute value and inequalities merge? They create an interesting topic absolute value inequalities. Surge ahead in solving the absolute value inequalities featured in our printable inequalities worksheets.

Quadratic Inequalities Worksheets

Inequalities involving the second degree taking precedence in these pdfs. Solve the quadratic inequalities, find the intervals that make the inequality true, graph the inequality by sketching the parabola are some exercises included here.

(18 Worksheets)

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- Introduction to Prerequisites
- 1.1 Real Numbers: Algebra Essentials
- 1.2 Exponents and Scientific Notation
- 1.3 Radicals and Rational Exponents
- 1.4 Polynomials
- 1.5 Factoring Polynomials
- 1.6 Rational Expressions
- Key Equations
- Key Concepts

## Review Exercises

Practice test.

- Introduction to Equations and Inequalities

## 2.1 The Rectangular Coordinate Systems and Graphs

2.2 linear equations in one variable, 2.3 models and applications, 2.4 complex numbers, 2.5 quadratic equations, 2.6 other types of equations, 2.7 linear inequalities and absolute value inequalities.

- Introduction to Functions
- 3.1 Functions and Function Notation
- 3.2 Domain and Range
- 3.3 Rates of Change and Behavior of Graphs
- 3.4 Composition of Functions
- 3.5 Transformation of Functions
- 3.6 Absolute Value Functions
- 3.7 Inverse Functions
- Introduction to Linear Functions
- 4.1 Linear Functions
- 4.2 Modeling with Linear Functions
- 4.3 Fitting Linear Models to Data
- Introduction to Polynomial and Rational Functions
- 5.1 Quadratic Functions
- 5.2 Power Functions and Polynomial Functions
- 5.3 Graphs of Polynomial Functions
- 5.4 Dividing Polynomials
- 5.5 Zeros of Polynomial Functions
- 5.6 Rational Functions
- 5.7 Inverses and Radical Functions
- 5.8 Modeling Using Variation
- Introduction to Exponential and Logarithmic Functions
- 6.1 Exponential Functions
- 6.2 Graphs of Exponential Functions
- 6.3 Logarithmic Functions
- 6.4 Graphs of Logarithmic Functions
- 6.5 Logarithmic Properties
- 6.6 Exponential and Logarithmic Equations
- 6.7 Exponential and Logarithmic Models
- 6.8 Fitting Exponential Models to Data
- Introduction to Systems of Equations and Inequalities
- 7.1 Systems of Linear Equations: Two Variables
- 7.2 Systems of Linear Equations: Three Variables
- 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
- 7.4 Partial Fractions
- 7.5 Matrices and Matrix Operations
- 7.6 Solving Systems with Gaussian Elimination
- 7.7 Solving Systems with Inverses
- 7.8 Solving Systems with Cramer's Rule
- Introduction to Analytic Geometry
- 8.1 The Ellipse
- 8.2 The Hyperbola
- 8.3 The Parabola
- 8.4 Rotation of Axes
- 8.5 Conic Sections in Polar Coordinates
- Introduction to Sequences, Probability and Counting Theory
- 9.1 Sequences and Their Notations
- 9.2 Arithmetic Sequences
- 9.3 Geometric Sequences
- 9.4 Series and Their Notations
- 9.5 Counting Principles
- 9.6 Binomial Theorem
- 9.7 Probability

x -intercept is ( 4 , 0 ) ; ( 4 , 0 ) ; y- intercept is ( 0 , 3 ) . ( 0 , 3 ) .

125 = 5 5 125 = 5 5

( − 5 , 5 2 ) ( − 5 , 5 2 )

x = −5 x = −5

x = −3 x = −3

x = 10 3 x = 10 3

x = 1 x = 1

x = − 7 17 . x = − 7 17 . Excluded values are x = − 1 2 x = − 1 2 and x = − 1 3 . x = − 1 3 .

x = 1 3 x = 1 3

m = − 2 3 m = − 2 3

y = 4 x −3 y = 4 x −3

x + 3 y = 2 x + 3 y = 2

Horizontal line: y = 2 y = 2

Parallel lines: equations are written in slope-intercept form.

y = 5 x + 3 y = 5 x + 3

C = 2.5 x + 3 , 650 C = 2.5 x + 3 , 650

L = 37 L = 37 cm, W = 18 W = 18 cm

−24 = 0 + 2 i 6 −24 = 0 + 2 i 6

( 3 −4 i ) − ( 2 + 5 i ) = 1 −9 i ( 3 −4 i ) − ( 2 + 5 i ) = 1 −9 i

5 2 − i 5 2 − i

18 + i 18 + i

−3 −4 i −3 −4 i

( x − 6 ) ( x + 1 ) = 0 ; x = 6 , x = − 1 ( x − 6 ) ( x + 1 ) = 0 ; x = 6 , x = − 1

( x −7 ) ( x + 3 ) = 0 , ( x −7 ) ( x + 3 ) = 0 , x = 7 , x = 7 , x = −3. x = −3.

( x + 5 ) ( x −5 ) = 0 , ( x + 5 ) ( x −5 ) = 0 , x = −5 , x = −5 , x = 5. x = 5.

( 3 x + 2 ) ( 4 x + 1 ) = 0 , ( 3 x + 2 ) ( 4 x + 1 ) = 0 , x = − 2 3 , x = − 2 3 , x = − 1 4 x = − 1 4

x = 0 , x = −10 , x = −1 x = 0 , x = −10 , x = −1

x = 4 ± 5 x = 4 ± 5

x = 3 ± 22 x = 3 ± 22

x = − 2 3 , x = − 2 3 , x = 1 3 x = 1 3

{ −1 } { −1 }

0 , 0 , 1 2 , 1 2 , − 1 2 − 1 2

1 ; 1 ; extraneous solution − 2 9 − 2 9

−2 ; −2 ; extraneous solution −1 −1

−1 , −1 , 3 2 3 2

−3 , 3 , − i , i −3 , 3 , − i , i

2 , 12 2 , 12

−1 , −1 , 0 0 is not a solution.

[ −3 , 5 ] [ −3 , 5 ]

( − ∞ , −2 ) ∪ [ 3 , ∞ ) ( − ∞ , −2 ) ∪ [ 3 , ∞ )

x < 1 x < 1

x ≥ −5 x ≥ −5

( 2 , ∞ ) ( 2 , ∞ )

[ − 3 14 , ∞ ) [ − 3 14 , ∞ )

6 < x ≤ 9 or ( 6 , 9 ] 6 < x ≤ 9 or ( 6 , 9 ]

( − 1 8 , 1 2 ) ( − 1 8 , 1 2 )

| x −2 | ≤ 3 | x −2 | ≤ 3

k ≤ 1 k ≤ 1 or k ≥ 7 ; k ≥ 7 ; in interval notation, this would be ( − ∞ , 1 ] ∪ [ 7 , ∞ ) . ( − ∞ , 1 ] ∪ [ 7 , ∞ ) .

## 2.1 Section Exercises

Answers may vary. Yes. It is possible for a point to be on the x -axis or on the y -axis and therefore is considered to NOT be in one of the quadrants.

The y -intercept is the point where the graph crosses the y -axis.

The x- intercept is ( 2 , 0 ) ( 2 , 0 ) and the y -intercept is ( 0 , 6 ) . ( 0 , 6 ) .

The x- intercept is ( 2 , 0 ) ( 2 , 0 ) and the y -intercept is ( 0 , −3 ) . ( 0 , −3 ) .

The x- intercept is ( 3 , 0 ) ( 3 , 0 ) and the y -intercept is ( 0 , 9 8 ) . ( 0 , 9 8 ) .

y = 4 − 2 x y = 4 − 2 x

y = 5 − 2 x 3 y = 5 − 2 x 3

y = 2 x − 4 5 y = 2 x − 4 5

d = 74 d = 74

d = 36 = 6 d = 36 = 6

d ≈ 62.97 d ≈ 62.97

( 3 , − 3 2 ) ( 3 , − 3 2 )

( 2 , −1 ) ( 2 , −1 )

( 0 , 0 ) ( 0 , 0 )

y = 0 y = 0

not collinear

A: ( −3 , 2 ) , B: ( 1 , 3 ) , C: ( 4 , 0 ) A: ( −3 , 2 ) , B: ( 1 , 3 ) , C: ( 4 , 0 )

d = 8.246 d = 8.246

d = 5 d = 5

( −3 , 4 ) ( −3 , 4 )

x = 0 y = −2 x = 0 y = −2

x = 0.75 y = 0 x = 0.75 y = 0

x = − 1.667 y = 0 x = − 1.667 y = 0

15 − 11.2 = 3.8 mi 15 − 11.2 = 3.8 mi shorter

6 .0 42 6 .0 42

Midpoint of each diagonal is the same point ( 2 , –2 ) ( 2 , –2 ) . Note this is a characteristic of rectangles, but not other quadrilaterals.

## 2.2 Section Exercises

It means they have the same slope.

The exponent of the x x variable is 1. It is called a first-degree equation.

If we insert either value into the equation, they make an expression in the equation undefined (zero in the denominator).

x = 2 x = 2

x = 2 7 x = 2 7

x = 6 x = 6

x = 3 x = 3

x = −14 x = −14

x ≠ −4 ; x ≠ −4 ; x = −3 x = −3

x ≠ 1 ; x ≠ 1 ; when we solve this we get x = 1 , x = 1 , which is excluded, therefore NO solution

x ≠ 0 ; x ≠ 0 ; x = − 5 2 x = − 5 2

y = − 4 5 x + 14 5 y = − 4 5 x + 14 5

y = − 3 4 x + 2 y = − 3 4 x + 2

y = 1 2 x + 5 2 y = 1 2 x + 5 2

y = −3 x − 5 y = −3 x − 5

y = 7 y = 7

y = −4 y = −4

8 x + 5 y = 7 8 x + 5 y = 7

Perpendicular

m = − 9 7 m = − 9 7

m = 3 2 m = 3 2

m 1 = − 1 3 , m 2 = 3 ; Perpendicular . m 1 = − 1 3 , m 2 = 3 ; Perpendicular .

y = 0.245 x − 45.662. y = 0.245 x − 45.662. Answers may vary. y min = −50 , y max = −40 y min = −50 , y max = −40

y = − 2.333 x + 6.667. y = − 2.333 x + 6.667. Answers may vary. y min = −10 , y max = 10 y min = −10 , y max = 10

y = − A B x + C B y = − A B x + C B

The slope for ( −1 , 1 ) to ( 0 , 4 ) is 3. The slope for ( −1 , 1 ) to ( 2 , 0 ) is − 1 3 . The slope for ( 2 , 0 ) to ( 3 , 3 ) is 3. The slope for ( 0 , 4 ) to ( 3 , 3 ) is − 1 3 . The slope for ( −1 , 1 ) to ( 0 , 4 ) is 3. The slope for ( −1 , 1 ) to ( 2 , 0 ) is − 1 3 . The slope for ( 2 , 0 ) to ( 3 , 3 ) is 3. The slope for ( 0 , 4 ) to ( 3 , 3 ) is − 1 3 .

Yes they are perpendicular.

## 2.3 Section Exercises

Answers may vary. Possible answers: We should define in words what our variable is representing. We should declare the variable. A heading.

2 , 000 − x 2 , 000 − x

v + 10 v + 10

Ann: 23 ; 23 ; Beth: 46 46

20 + 0.05 m 20 + 0.05 m

90 + 40 P 90 + 40 P

50 , 000 − x 50 , 000 − x

She traveled for 2 h at 20 mi/h, or 40 miles.

$5,000 at 8% and $15,000 at 12%

B = 100 + .05 x B = 100 + .05 x

R = 9 R = 9

r = 4 5 r = 4 5 or 0.8

W = P − 2 L 2 = 58 − 2 ( 15 ) 2 = 14 W = P − 2 L 2 = 58 − 2 ( 15 ) 2 = 14

f = p q p + q = 8 ( 13 ) 8 + 13 = 104 21 f = p q p + q = 8 ( 13 ) 8 + 13 = 104 21

m = − 5 4 m = − 5 4

h = 2 A b 1 + b 2 h = 2 A b 1 + b 2

length = 360 ft; width = 160 ft

A = 88 in . 2 A = 88 in . 2

h = V π r 2 h = V π r 2

r = V π h r = V π h

C = 12 π C = 12 π

## 2.4 Section Exercises

Add the real parts together and the imaginary parts together.

Possible answer: i i times i i equals -1, which is not imaginary.

−8 + 2 i −8 + 2 i

14 + 7 i 14 + 7 i

− 23 29 + 15 29 i − 23 29 + 15 29 i

8 − i 8 − i

−11 + 4 i −11 + 4 i

2 −5 i 2 −5 i

6 + 15 i 6 + 15 i

−16 + 32 i −16 + 32 i

−4 −7 i −4 −7 i

2 − 2 3 i 2 − 2 3 i

4 − 6 i 4 − 6 i

2 5 + 11 5 i 2 5 + 11 5 i

1 + i 3 1 + i 3

( 3 2 + 1 2 i ) 6 = −1 ( 3 2 + 1 2 i ) 6 = −1

5 −5 i 5 −5 i

9 2 − 9 2 i 9 2 − 9 2 i

## 2.5 Section Exercises

It is a second-degree equation (the highest variable exponent is 2).

We want to take advantage of the zero property of multiplication in the fact that if a ⋅ b = 0 a ⋅ b = 0 then it must follow that each factor separately offers a solution to the product being zero: a = 0 o r b = 0. a = 0 o r b = 0.

One, when no linear term is present (no x term), such as x 2 = 16. x 2 = 16. Two, when the equation is already in the form ( a x + b ) 2 = d . ( a x + b ) 2 = d .

x = 6 , x = 6 , x = 3 x = 3

x = − 5 2 , x = − 5 2 , x = − 1 3 x = − 1 3

x = 5 , x = 5 , x = −5 x = −5

x = − 3 2 , x = − 3 2 , x = 3 2 x = 3 2

x = −2 , 3 x = −2 , 3

x = 0 , x = 0 , x = − 3 7 x = − 3 7

x = −6 , x = −6 , x = 6 x = 6

x = 6 , x = 6 , x = −4 x = −4

x = 1 , x = 1 , x = −2 x = −2

x = −2 , x = −2 , x = 11 x = 11

z = 2 3 , z = 2 3 , z = − 1 2 z = − 1 2

x = 3 ± 17 4 x = 3 ± 17 4

One rational

Two real; rational

x = − 1 ± 17 2 x = − 1 ± 17 2

x = 5 ± 13 6 x = 5 ± 13 6

x = − 1 ± 17 8 x = − 1 ± 17 8

x ≈ 0.131 x ≈ 0.131 and x ≈ 2.535 x ≈ 2.535

x ≈ − 6.7 x ≈ − 6.7 and x ≈ 1.7 x ≈ 1.7

a x 2 + b x + c = 0 x 2 + b a x = − c a x 2 + b a x + b 2 4 a 2 = − c a + b 4 a 2 ( x + b 2 a ) 2 = b 2 − 4 a c 4 a 2 x + b 2 a = ± b 2 − 4 a c 4 a 2 x = − b ± b 2 − 4 a c 2 a a x 2 + b x + c = 0 x 2 + b a x = − c a x 2 + b a x + b 2 4 a 2 = − c a + b 4 a 2 ( x + b 2 a ) 2 = b 2 − 4 a c 4 a 2 x + b 2 a = ± b 2 − 4 a c 4 a 2 x = − b ± b 2 − 4 a c 2 a

x ( x + 10 ) = 119 ; x ( x + 10 ) = 119 ; 7 ft. and 17 ft.

maximum at x = 70 x = 70

The quadratic equation would be ( 100 x −0.5 x 2 ) − ( 60 x + 300 ) = 300. ( 100 x −0.5 x 2 ) − ( 60 x + 300 ) = 300. The two values of x x are 20 and 60.

## 2.6 Section Exercises

This is not a solution to the radical equation, it is a value obtained from squaring both sides and thus changing the signs of an equation which has caused it not to be a solution in the original equation.

He or she is probably trying to enter negative 9, but taking the square root of −9 −9 is not a real number. The negative sign is in front of this, so your friend should be taking the square root of 9, cubing it, and then putting the negative sign in front, resulting in −27. −27.

A rational exponent is a fraction: the denominator of the fraction is the root or index number and the numerator is the power to which it is raised.

x = 81 x = 81

x = 17 x = 17

x = 8 , x = 27 x = 8 , x = 27

x = −2 , 1 , −1 x = −2 , 1 , −1

y = 0 , 3 2 , − 3 2 y = 0 , 3 2 , − 3 2

m = 1 , −1 m = 1 , −1

x = 2 5 , ±3 i x = 2 5 , ±3 i

x = 32 x = 32

t = 44 3 t = 44 3

x = −2 x = −2

x = 4 , −4 3 x = 4 , −4 3

x = − 5 4 , 7 4 x = − 5 4 , 7 4

x = 3 , −2 x = 3 , −2

x = 1 , −1 , 3 , -3 x = 1 , −1 , 3 , -3

x = 2 , −2 x = 2 , −2

x = 1 , 5 x = 1 , 5

x ≥ 0 x ≥ 0

x = 4 , 6 , −6 , −8 x = 4 , 6 , −6 , −8

## 2.7 Section Exercises

When we divide both sides by a negative it changes the sign of both sides so the sense of the inequality sign changes.

( − ∞ , ∞ ) ( − ∞ , ∞ )

We start by finding the x -intercept, or where the function = 0. Once we have that point, which is ( 3 , 0 ) , ( 3 , 0 ) , we graph to the right the straight line graph y = x −3 , y = x −3 , and then when we draw it to the left we plot positive y values, taking the absolute value of them.

( − ∞ , 3 4 ] ( − ∞ , 3 4 ]

[ − 13 2 , ∞ ) [ − 13 2 , ∞ )

( − ∞ , 3 ) ( − ∞ , 3 )

( − ∞ , − 37 3 ] ( − ∞ , − 37 3 ]

All real numbers ( − ∞ , ∞ ) ( − ∞ , ∞ )

( − ∞ , − 10 3 ) ∪ ( 4 , ∞ ) ( − ∞ , − 10 3 ) ∪ ( 4 , ∞ )

( − ∞ , −4 ] ∪ [ 8 , + ∞ ) ( − ∞ , −4 ] ∪ [ 8 , + ∞ )

No solution

( −5 , 11 ) ( −5 , 11 )

[ 6 , 12 ] [ 6 , 12 ]

[ −10 , 12 ] [ −10 , 12 ]

x > − 6 and x > − 2 Take the intersection of two sets . x > − 2 , ( − 2 , + ∞ ) x > − 6 and x > − 2 Take the intersection of two sets . x > − 2 , ( − 2 , + ∞ )

x < − 3 or x ≥ 1 Take the union of the two sets . ( − ∞ , − 3 ) ∪ [ 1 , ∞ ) x < − 3 or x ≥ 1 Take the union of the two sets . ( − ∞ , − 3 ) ∪ [ 1 , ∞ )

( − ∞ , −1 ) ∪ ( 3 , ∞ ) ( − ∞ , −1 ) ∪ ( 3 , ∞ )

[ −11 , −3 ] [ −11 , −3 ]

It is never less than zero. No solution.

Where the blue line is above the orange line; point of intersection is x = − 3. x = − 3.

( − ∞ , −3 ) ( − ∞ , −3 )

Where the blue line is above the orange line; always. All real numbers.

( − ∞ , − ∞ ) ( − ∞ , − ∞ )

( −1 , 3 ) ( −1 , 3 )

( − ∞ , 4 ) ( − ∞ , 4 )

{ x | x < 6 } { x | x < 6 }

{ x | −3 ≤ x < 5 } { x | −3 ≤ x < 5 }

( −2 , 1 ] ( −2 , 1 ]

( − ∞ , 4 ] ( − ∞ , 4 ]

Where the blue is below the orange; always. All real numbers. ( − ∞ , + ∞ ) . ( − ∞ , + ∞ ) .

Where the blue is below the orange; ( 1 , 7 ) . ( 1 , 7 ) .

x = 2 , − 4 5 x = 2 , − 4 5

( −7 , 5 ] ( −7 , 5 ]

80 ≤ T ≤ 120 1 , 600 ≤ 20 T ≤ 2 , 400 80 ≤ T ≤ 120 1 , 600 ≤ 20 T ≤ 2 , 400

[ 1 , 600 , 2 , 400 ] [ 1 , 600 , 2 , 400 ]

x -intercept: ( 3 , 0 ) ; ( 3 , 0 ) ; y -intercept: ( 0 , −4 ) ( 0 , −4 )

y = 5 3 x + 4 y = 5 3 x + 4

72 = 6 2 72 = 6 2

620.097 620.097

midpoint is ( 2 , 23 2 ) ( 2 , 23 2 )

x = 4 x = 4

x = 12 7 x = 12 7

y = 1 6 x + 4 3 y = 1 6 x + 4 3

y = 2 3 x + 6 y = 2 3 x + 6

females 17, males 56

x = − 3 4 ± i 47 4 x = − 3 4 ± i 47 4

horizontal component −2 ; −2 ; vertical component −1 −1

7 + 11 i 7 + 11 i

−16 − 30 i −16 − 30 i

−4 − i 10 −4 − i 10

x = 7 − 3 i x = 7 − 3 i

x = −1 , −5 x = −1 , −5

x = 0 , 9 7 x = 0 , 9 7

x = 10 , −2 x = 10 , −2

x = − 1 ± 5 4 x = − 1 ± 5 4

x = 2 5 , − 1 3 x = 2 5 , − 1 3

x = 5 ± 2 7 x = 5 ± 2 7

x = 0 , 256 x = 0 , 256

x = 0 , ± 2 x = 0 , ± 2

x = 11 2 , −17 2 x = 11 2 , −17 2

[ − 10 3 , 2 ] [ − 10 3 , 2 ]

( − 4 3 , 1 5 ) ( − 4 3 , 1 5 )

Where the blue is below the orange line; point of intersection is x = 3.5. x = 3.5.

( 3.5 , ∞ ) ( 3.5 , ∞ )

y = 3 2 x + 2 y = 3 2 x + 2

( 0 , −3 ) ( 0 , −3 ) ( 4 , 0 ) ( 4 , 0 )

( − ∞ , 9 ] ( − ∞ , 9 ]

x = −15 x = −15

x ≠ −4 , 2 ; x ≠ −4 , 2 ; x = − 5 2 , 1 x = − 5 2 , 1

x = 3 ± 3 2 x = 3 ± 3 2

( −4 , 1 ) ( −4 , 1 )

y = −5 9 x − 2 9 y = −5 9 x − 2 9

y = 5 2 x − 4 y = 5 2 x − 4

5 13 − 14 13 i 5 13 − 14 13 i

x = 2 , − 4 3 x = 2 , − 4 3

x = 1 2 ± 2 2 x = 1 2 ± 2 2

x = 1 2 , 2 , −2 x = 1 2 , 2 , −2

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- Authors: Jay Abramson
- Publisher/website: OpenStax
- Book title: College Algebra
- Publication date: Feb 13, 2015
- Location: Houston, Texas
- Book URL: https://openstax.org/books/college-algebra/pages/1-introduction-to-prerequisites
- Section URL: https://openstax.org/books/college-algebra/pages/chapter-2

© Dec 8, 2021 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

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The topics have been divided up by day and are listed below and in the table of contents on the 2nd page. Lesson 1: Solve Absolute Value Equations Lesson 2: Solve Absolute Value Inequalities Lesson 3: Solve and Graph Quadratic Inequalities Lesson 4: Solve Rational Inequalities Homework answers are provided at the end of the unit.

Quiz Unit test About this unit Solving equations is a superpower. It means we can model a situation with an equation in any way that makes sense to us, even with an unknown value in the middle. Inequalities are for situations with many true options, like how many pages I can send in my letter using just 1 stamp. Algebraic equations basics Learn

Algebra 1 16 units · 184 skills. Unit 1 Algebra foundations. Unit 2 Solving equations & inequalities. Unit 3 Working with units. Unit 4 Linear equations & graphs. Unit 5 Forms of linear equations. Unit 6 Systems of equations. Unit 7 Inequalities (systems & graphs) Unit 8 Functions.

Unit 4 Percentages. Unit 5 Exponents intro and order of operations. Unit 6 Variables & expressions. Unit 7 Equations & inequalities introduction. Unit 8 Percent & rational number word problems. Unit 9 Proportional relationships. Unit 10 One-step and two-step equations & inequalities. Unit 11 Roots, exponents, & scientific notation.

Finding and Graphing Solution Sets of Inequalities. Home Link 4-10 English Español Selected Answers. 4-11. Inequalities to Represent Real-World Situations ... Unit 4 Progress Check. ... With a login provided by your child's teacher, access resources to help your child with homework or brush up on your math skills.

Only has to fit when plugging in ONE equation. steps to solving abs. value in equalities. 1) Isolate the abs. value. 2) Determine if it's "and or "or". 3) Rewrite as compound inequality. 4) Solve. 5) Graph. 6) Check. Study with Quizlet and memorize flashcards containing terms like <, >, ≥ and more.

Two Step Inequalities Worksheets. Refine your skills in solving and graphing inequalities in two simple steps. Grade 7 students separate the like terms on either side of the inequality. Use inverse operations to isolate the variable and solving the inequality will be duck soup. (51 Worksheets)

Level up on all the skills in this unit and collect up to 1000 Mastery points! Start Unit test. In this unit, we learn how to solve linear equations and inequalities that contain a single variable. For example, we'll solve equations like 2 (x+3)= (4x-1)/2+7 and inequalities like 5x-2≥2 (x-1).

Graphing linear inequality in TWO variables. 1. Graph the line. 2. Decide if the line is dotted or solid. 3. Shading using a test point - Test a point not on the line. Shade the side of the line away from the point tested if the test is false. Shade the side of the line with the point tested if the test is true.

The Algebra 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; and Quadratic equations, functions, and graphs. Khan Academy's Algebra 1 course is built to deliver a comprehensive, illuminating, engaging, and Common Core aligned experience!

Table of Contents for Common Core Algebra I. Unit 1 - The Building Blocks of Algebra. Unit 2 - Linear Expressions, Equations, and Inequalities. Unit 3 - Functions. Unit 4 - Linear Functions and Arithmetic Sequences. In this course students will explore a variety of topics within algebra including linear, exponential, quadratic, and polynomial ...

inequality to remind me to change it on the next line!! x < − 5. Check: 2 4 x <− −. 4 x 1 4 − • − −2(−4) When I multiplied both sides by −4, I circled <!! Circling the inequality helps me to remember to change x > 8 the direction of the inequality. Check: You try. Solve and graph. or dividing by a negative number, flip the ...

Homework 4: Solving Multi-Step Inequalities Monday December 10, 2018 Review Homework 5: Solving Inequalities Review Tuesday December 11, 2018 QUIZ Solve Compound Inequalities p. 10 - 11 Homework 6: Solving Compound Inequalities Wednesday December 12, 2018 Solve Absolute Value Equations and Inequalities p. 12 - 13 Homework 7:

Unit 5 - Systems of Linear Equations and Inequalities. This unit begins by ensuring that students understand that solutions to equations are points that make the equation true, while solutions to systems make all equations (or inequalities) true. Graphical and substitution methods for solving systems are reviewed before the development of the ...

Algebra (all content) 20 units · 412 skills. Unit 1 Introduction to algebra. Unit 2 Solving basic equations & inequalities (one variable, linear) Unit 3 Linear equations, functions, & graphs. Unit 4 Sequences. Unit 5 System of equations. Unit 6 Two-variable inequalities. Unit 7 Functions. Unit 8 Absolute value equations, functions, & inequalities.

Unit: Equations & Inequalities Homework 8 Name Date SOLVING INEQUALITIES Solve the following one-step inequalities, check your work, and graph the solution. ex < 54 v' CHECK. v' CHECK: v' CHECK. Use your understanding of inequalities to answer the questions below. D. 18 < x -8 4. 5. 6. C.

Unit 4 Equations and Inequalities; Unit 5 Systems of Equations and Inequalities; Unit 6 Quadratic Functions; Unit 7 Structures of Quadratic Expressions; Unit 8 More Functions, More Features; Unit 9 Modeling Data; Open Up HS Math is published as an Open Educational Resource.

Homework 11/27 4.1 - Solving Systems of Equations by Graphing (Checking Solutions, Finding Solutions by Graphing) ... 4.5 - Graphing Systems of Inequalities 4.5 Day 2 Worksheet ... 4.3-4.5 Quiz Review 12/13 4.3-4.5 Quiz None 12/14 4.6 - System of Inequalities Application 4.6 Worksheet 12/15 Unit 4 Review ...

Unit: Inequalities Homework 2 Name Date ONE-STEP INEQUALITIES Solve the following one-step inequalities, check your work, and graph the solution. 3x < 54 v' CHECK. v' CHECK. x -7>2q v' CHECK. D. 18 < x -8 Use your understanding of inequalities to answer the questions below. 4. 5. 6. C.

solve multi-step linear inequalities including those with variables on both sides ready-to-go, scaffolded student materials student friendly + real-world application scaffolded concepts self-checking practice streamline your planning process with unit overviews key vocabulary vertical alignment sample pacing calendar teaching ideas

2.1 Section Exercises. 1. Answers may vary. Yes. It is possible for a point to be on the x -axis or on the y -axis and therefore is considered to NOT be in one of the quadrants. 3. The y -intercept is the point where the graph crosses the y -axis. 5. The x- intercept is ( 2, 0 ) and the y -intercept is ( 0, 6 ). 7.

Steps to solving quadratic inequalities. Step 1. Rewrite the inequality so that a x 2 + b x + c is on one side and zero is on the other. Step 2. Determine where the inequality is zero using any method appropriate. Step 3. Use the x -values obtained in the previous step to label on a number line. Step 4.