Absolute Value Equations and Inequalities

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|.

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x = 12 and x = 0

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Back

x = -1 and x = 4

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What does it mean when an absolute value equation has no solution?

Back

It means that there are no values of x that can satisfy the equation, often because the expression inside the absolute value cannot equal a negative number.

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No Solution

Front

What is the proper inequality solution for the graph showing x ≤ -7 or x ≥ 3?

Back

The solution represents values of x that are either less than or equal to -7 or greater than or equal to 3.

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Back

This inequality indicates that the values of x are either greater than or equal to 3 or less than or equal to -7.

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What is the general form of an absolute value equation?

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An absolute value equation is typically in the form |A| = B, where A is an expression and B is a non-negative number.

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How do you solve an absolute value inequality?

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To solve an absolute value inequality, split it into two cases: one for the positive scenario and one for the negative scenario.

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The solution set is -3 < x < 3.