3 - 4 Solving Absolute Value Equations and Inequalities

Front

What is an 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 equation of the form |x| = a, you set up two separate equations: x = a and x = -a.

Front

What does the inequality |x| < a represent?

Back

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

Front

What does the inequality |x| > a represent?

Back

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

Front

Solve the equation |x - 5| = 3.

Back

x - 5 = 3 or x - 5 = -3, so x = 8 or x = 2.

Front

Solve the inequality |x + 2| < 4.

Back

-4 < x + 2 < 4, which simplifies to -6 < x < 2.

Front

Solve the inequality |2x - 1| > 5.

Back

2x - 1 > 5 or 2x - 1 < -5, leading to x > 3 or x < -2.

Front

What is the solution to |b - 8| + 10 > 22?

Back

b < -4 or b > 20.

Front

Solve the equation |x + 3| > 8.

Back

x > 5 or x < -11.

Front

What is the solution to |v + 8| - 5 = 2?

Back

v = -15 or v = -1.