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