Absolute Value Inequalities Review

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What is the absolute value of a number?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.

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How do you solve an absolute value inequality of the form |x - a| > b?

Back

To solve |x - a| > b, you create two inequalities: x - a > b or x - a < -b.

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How do you solve an absolute value inequality of the form |x - a| < b?

Back

To solve |x - a| < b, you create one compound inequality: -b < x - a < b.

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What does it mean if an absolute value inequality has an 'and' condition?

Back

An 'and' condition means that the solution must satisfy both parts of the inequality simultaneously.

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What does it mean if an absolute value inequality has an 'or' condition?

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An 'or' condition means that the solution can satisfy either part of the inequality.

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What is the first step in solving |3x + 5| < 12?

Back

The first step is to set up the compound inequality: -12 < 3x + 5 < 12.

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What is the solution to the inequality |x - 4| > 6?

Back

The solution is x < -2 or x > 10.

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What is the solution to the inequality |2x + 3| < 5?

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The solution is -4 < 2x + 3 < 4, which simplifies to -3 < x < 0.5.

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

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It means that there are no values of the variable that can satisfy the equation.

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What is the graphical representation of an absolute value inequality?

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The graphical representation shows a number line with shaded regions indicating the solution set.