Absolute Value Inequalities

Front

What is the definition of absolute value?

Back

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

Front

How do you solve an absolute value inequality of the form |x| < a?

Back

To solve |x| < a, split it into two inequalities: -a < x < a.

Front

How do you solve an absolute value inequality of the form |x| > a?

Back

To solve |x| > a, split it into two inequalities: x < -a or x > a.

Front

What does the inequality |x - 4| < -3 represent?

Back

This inequality has no solution because absolute values cannot be negative.

Front

What is the first step in solving |2x + 7| - 7 < -4?

Back

Get the absolute value alone by adding 7 to both sides.

Front

What does the solution x < -3 and x > -4 represent?

Back

This represents a range of values for x that satisfy the inequality.

Front

What is the solution to |x + 3| > 8?

Back

x > 5 or x < -11.

Front

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

Back

It means that the solution includes values from two separate ranges.

Front

What is the graphical representation of |x - 2| > 3?

Back

It consists of two rays extending from the points x = 5 and x = -1 on the number line.

Front

How do you interpret the solution x < -3 and x > -4?

Back

It means x can take any value less than -3 or any value greater than -4.