Absolute Value Equations and Inequalities

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 |A| = B, set up two equations: A = B and A = -B, then solve for the variable.

Front

Solve the absolute value equation: |4x - 3| = 1

Back

x = 1, x = 0.5

Front

Solve the absolute value equation: |5x + 1| = 9

Back

x = 8/5, x = -2

Front

What does it mean when an absolute value inequality is written as |A| < B?

Back

It means that the expression A is within B units of 0, leading to two inequalities: -B < A < B.

Front

Solve the absolute value inequality: |2x - 3| < 5

Back

-1 < x < 4

Front

What does it mean when an absolute value inequality is written as |A| > B?

Back

It means that the expression A is more than B units away from 0, leading to two inequalities: A < -B or A > B.

Front

Solve the absolute value inequality: |3x + 4| > 8

Back

x < -4 or x > 4/3

Front

Solve the absolute value equation: |2x - 5| = 7

Back

x = 6, x = -1

Front

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

Back

Isolate the absolute value expression on one side of the equation.