Absolute Value Inequalities

Front

What is an absolute value inequality?

Back

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

Front

How do you isolate the absolute value in an inequality?

Back

You can isolate the absolute value by performing inverse operations, such as adding, subtracting, multiplying, or dividing both sides of the inequality.

Front

What does |x| < a mean?

Back

It means that x is within a distance of a from 0, or -a < x < a.

Front

What does |x| > a mean?

Back

It means that x is outside the distance of a from 0, or x < -a or x > a.

Front

How do you solve |x - 4| > 5?

Back

You create two inequalities: x - 4 > 5 or x - 4 < -5, which simplifies to x > 9 or x < -1.

Front

What is the first step in solving |2x + 3| < 7?

Back

Isolate the absolute value by setting up the inequalities: -7 < 2x + 3 < 7.

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

Back

The solution is -5 < x < 1.

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What is the solution to |x - 1| > 4?

Back

The solution is x < -3 or x > 5.

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

Back

The solution represents a range of values that satisfy the inequality, indicating where the variable lies in relation to a certain distance.

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

Back

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