Absolute Value Equations and Inequalities

Absolute Value Equations and Inequalities

Assessment

Flashcard

Mathematics

8th - 9th Grade

Practice Problem

Hard

Created by

Wayground Content

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

2.

FLASHCARD QUESTION

Front

How do you solve an absolute value equation?

Back

To solve an absolute value equation, set the expression inside the absolute value equal to both the positive and negative values of the other side of the equation.

3.

FLASHCARD QUESTION

Front

What does the inequality |x| < a represent?

Back

It represents that x is within a distance a from 0, meaning -a < x < a.

4.

FLASHCARD QUESTION

Front

What does the inequality |x| > a represent?

Back

It represents that x is outside a distance a from 0, meaning x < -a or x > a.

5.

FLASHCARD QUESTION

Front

How do you graph the solution of an absolute value inequality?

Back

Graph the critical points found from the inequality and use open or closed circles based on whether the inequality is strict (<, >) or inclusive (≤, ≥).

6.

FLASHCARD QUESTION

Front

What is the solution to the equation |x - 3| = 5?

Back

x - 3 = 5 or x - 3 = -5, leading to x = 8 or x = -2.

7.

FLASHCARD QUESTION

Front

What is the solution to the inequality |2x + 1| ≤ 3?

Back

-4 ≤ 2x ≤ 2, leading to -2 ≤ x ≤ 1.

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