Absolute Value Mastery

A Grade 12 mathematics worksheet focusing on understanding and applying absolute value concepts, equations, and inequalities.

Grade 12 Math Number SenseIntegers and Rational NumbersAbsolute Value

Use This Worksheet

Includes

Fill in the Blanks3 Short AnswerMultiple ChoiceTrue / FalseMatching

Standards

CCSS.MATH.CONTENT.HSA.CED.A.1CCSS.MATH.CONTENT.HSA.REI.B.3CCSS.MATH.CONTENT.HSN.RN.A.2

Topics

absolute valueequationsinequalitiesnumber linealgebra

9 sections · Free to use · Printable

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Date:

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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. The absolute value of a number represents its from zero on the number line.

2. For any real number x, |x| ≥ .

3. If |x| = 5, then x can be or .

1. Illustrate on the number line the solution set for |x| < 3.

2. What is the distance between -7 and 2 on the number line? Express your answer using absolute value notation.

1. What are the solutions to the equation |2x - 1| = 7?

x = 4, x = -3

x = -4, x = 3

x = 4, x = 3

x = -4, x = -3

1. Solve for x: |3x + 5| = 14

2. Find the values of y that satisfy the equation |-y + 8| = 2.

1. The inequality |x| > 4 represents all numbers x such that x > 4 or x < -4.

True

False

1. Solve the inequality |x - 6| ≤ 2 and express your answer in interval notation.

2. Determine the solution set for |2x + 3| > 5. Graph your solution on a number line.

Match each property with its description.

1. |a · b|

a. Triangle Inequality

2. |a / b|

b. Product Property

3. |a + b| ≤ |a| + |b|

c. Quotient Property