2.6 Solving Absolute Value Inequalities

Front

What is an absolute value inequality?

Back

An absolute value inequality is an inequality that contains an absolute value expression, which measures the distance of a number from zero on the number line.

Front

How do you solve the inequality |x| < a?

Back

To solve |x| < a, split it into two inequalities: -a < x < a.

Front

How do you solve the inequality |x| > a?

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To solve |x| > a, split it into two inequalities: x < -a or x > a.

Front

What does the solution |x| ≤ 3.5 represent?

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The solution -3.5 ≤ x ≤ 3.5 represents all values of x that are within 3.5 units from zero.

Front

What does the solution |3c - 5| < -2 indicate?

Back

The solution indicates 'No Solution' because absolute values cannot be negative.

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What is the first step in solving the inequality 3|d + 1| - 7 ≥ -1?

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The first step is to isolate the absolute value expression: 3|d + 1| ≥ 6.

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What is the significance of the 'or' in the solution d ≤ -3 or d ≥ 1?

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The 'or' indicates that either condition can satisfy the inequality, meaning both ranges are valid solutions.

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

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To graph the solution, plot the critical points on a number line and shade the appropriate regions based on the inequality.

Front

What is the solution to the inequality 3|2t - 3| - 5 > 16?

Back

The solution is t < -2 or t > 5.

Front

What does it mean if an absolute value inequality has 'All Real Numbers' as a solution?

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It means that any real number satisfies the inequality.