1.5 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

What does |x| < a mean?

Back

It means that the distance of x from 0 is less than a, which translates to -a < x < a.

Front

What does |x| > a mean?

Back

It means that the distance of x from 0 is greater than a, which translates to x < -a or x > a.

Front

What is the solution to |k - 3| < -1?

Back

No Solution, because absolute values cannot be negative.

Front

What is the solution to |2t - 3| > 7?

Back

t < -2 or t > 5.

Front

What is the solution to |3c - 5| < -2?

Back

No Solution, because absolute values cannot be negative.

Front

What does |x| ≤ 3.5 mean?

Back

It means that x is between -3.5 and 3.5, inclusive: -3.5 ≤ x ≤ 3.5.

Front

What is the solution to |2w - 1| < 11?

Back

-5 < w < 6.

Front

How do you solve an absolute value inequality?

Back

1. Isolate the absolute value expression. 2. Set up two separate inequalities based on the definition of absolute value. 3. Solve each inequality.

Front

What is the graphical representation of |x| < a?

Back

A number line showing an open interval from -a to a.