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

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 expression |x - c| ≤ d represent?

Back

It represents all values of x that are within d units of c on the number line.

Front

What does the expression |x - c| ≥ d represent?

Back

It represents all values of x that are at least d units away from c on the number line.

Front

Solve the inequality: |2x + 3| < 7.

Back

-5 < 2x + 3 < 7, which simplifies to -4 < x < 2.

Front

Solve the inequality: |x - 4| > 3.

Back

x < 1 or x > 7.

Front

What is the graphical representation of |x| < 3?

Back

The graph shows an open interval from -3 to 3 on the number line.

Front

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

Back

The graph shows two rays extending from -2 to the left and from 2 to the right.

Front

How do you express the solution of |x + 5| ≤ 4 in interval notation?

Back

The solution is expressed as [-9, -1].