Absolute Value Inequalities

Front

What is absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by |x|.

Front

How do you solve an absolute value inequality?

Back

To solve an absolute value inequality, you split it into two separate inequalities, one for the positive case and one for the negative case.

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 more than a distance of a from 0, or x < -a or x > a.

Front

What is the first step in solving |x - 5| < 3?

Back

Split it into two inequalities: x - 5 < 3 and x - 5 > -3.

Front

Solve: |x + 2| < 4

Back

-2 < x < 2.

Front

Solve: |3x - 1| > 5

Back

x < -rac{4}{3} or x > 2.

Front

What is the solution to |x| = 7?

Back

x = 7 or x = -7.

Front

How do you graph the solution of |x| < 3?

Back

Draw a number line and shade the region between -3 and 3, not including the endpoints.

Front

What is the difference between |x| < a and |x| > a?

Back

|x| < a indicates a range of values within a distance of a from 0, while |x| > a indicates values outside that distance.