Absolute Value Equations and Inequalities

Front

What is the definition of absolute value?

Back

The distance of a number from zero.

Front

Solve for x: |x| = 5

Back

x = -5 or x = 5

Front

Solve for x: |2x - 3| = 7

Back

x = 5 or x = -2

Front

What does the equation |x - a| = b represent?

Back

It represents two equations: x - a = b and x - a = -b.

Front

Solve for x: |x + 4| + 2 = 6

Back

x = -2 or x = -6

Front

What is the first step in solving an absolute value equation?

Back

Isolate the absolute value expression.

Front

Solve for x: |3x + 1| = 4

Back

x = 1 or x = - \frac{5}{3}.

Front

What is the solution set for |x| < 3?

Back

-3 < x < 3.

Front

Solve for x: |x - 2| < 5

Back

-3 < x < 7.

Front

What is the graphical representation of an absolute value function?

Back

A V-shaped graph that opens upwards.