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

How do you solve the inequality |x| < a?

Back

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

Front

How do you solve the inequality |x| > a?

Back

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

Front

What does the solution |y - 1| ≤ 6 represent?

Back

The solution -5 ≤ y ≤ 7 represents all values of y that are within 6 units of 1 on the number line.

Front

What does the solution |x + 4| < 5 represent?

Back

The solution -9 < x < 1 represents all values of x that are less than 5 units away from -4.

Front

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

Back

The graphical representation is an open interval on the number line between -a and a.

Front

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

Back

The graphical representation consists of two rays extending from -a to the left and from a to the right on the number line.

Front

Solve: |x - 3| < 8

Back

-5 < x < 11

Front

Solve: |x + 3| > 8

Back

x > 5 or x < -11

Front

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

Back

|x| < a indicates values within a distance a from zero, while |x| > a indicates values outside that distance.