Absolute Value Equations/Inequalites

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 equation?

Back

To solve an absolute value equation, set the expression inside the absolute value equal to both the positive and negative of the other side of the equation.

Front

What is the solution to |x| = a where a > 0?

Back

The solutions are x = a and x = -a.

Front

What does the inequality |x| < a represent?

Back

It represents all values of x that are within a distance a from 0 on the number line.

Front

What does the inequality |x| > a represent?

Back

It represents all values of x that are more than a distance a from 0 on the number line.

Front

Solve: |x - 3| = 5

Back

x = 8 or x = -2.

Front

Solve: |2x + 1| < 3

Back

-2 < x < 1.

Front

Solve: |x + 4| ≥ 6

Back

x ≤ -10 or x ≥ 2.

Front

What is the solution to the equation |−2n| - 30 = −20?

Back

The solutions are n = -5 and n = 5.

Front

Solve: 3|d - 4| ≥ 12

Back

d ≥ 8 or d ≤ 0.