Solve absolute value inequalities Review

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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.

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What does the symbol |x| represent?

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The symbol |x| represents the absolute value of x, which is the distance of x from 0 on the number line.

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How do you solve the inequality |x - 2| > 3?

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To solve |x - 2| > 3, split it into two inequalities: x - 2 > 3 or x - 2 < -3. This gives x > 5 or x < -1.

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What is the solution to the inequality |y - 4| ≥ 8?

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The solution is y ≤ -4 or y ≥ 12.

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What does it mean if an absolute value inequality is an 'or' problem?

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An 'or' problem means that the solution includes values that satisfy either of the conditions derived from the inequality.

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How do you express the solution of an absolute value inequality in interval notation?

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The solution can be expressed in interval notation, which uses brackets [ ] for inclusive and parentheses ( ) for exclusive intervals.

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What is the solution to the inequality -5|x - 4| > -20?

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The solution is x < 8 and x > 0.

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What does the graph of |x + 3| > 8 look like?

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The graph consists of two rays extending from the points x = 5 and x = -11, indicating the solution x > 5 or x < -11.

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What is the difference between 'and' and 'or' in absolute value inequalities?

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'And' indicates that both conditions must be true simultaneously, while 'or' indicates that at least one condition must be true.

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How do you determine if an absolute value inequality is 'and' or 'or'?

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If the inequality is of the form |x| < a, it is 'and'; if it is |x| > a, it is 'or'.