1.5 Solving Absolute Value Inequalities

Front

What is an absolute value inequality?

Back

An absolute value inequality is an inequality that involves the absolute value of a variable expression, indicating the distance of the expression from zero on a number line.

Front

What does |x| < a mean?

Back

It means that the value of x is within a distance of a from 0, resulting in the compound inequality -a < x < a.

Front

What does |x| > a mean?

Back

It means that the value of x is more than a distance of a from 0, resulting in the compound inequalities 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 |2w - 1| < 11?

Back

-5 < w < 6.

Front

What is the solution to |12 + w| ≥ -5?

Back

All Real Numbers, because absolute values are always non-negative.

Front

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

Back

No Solution, because absolute values cannot be negative.

Front

What does |x| ≤ 3.5 represent?

Back

It represents the values of x that are within 3.5 units from 0, resulting in the compound inequality -3.5 ≤ x ≤ 3.5.

Front

How do you solve |x| < a?

Back

Set up the compound inequality -a < x < a and solve for x.

Front

How do you solve |x| > a?

Back

Set up the compound inequalities x < -a or x > a and solve for x.