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

Solve the equation: |x| = 5

Back

x = 5 or x = -5.

Front

What does the equation |x - 3| = 7 represent?

Back

It represents two equations: x - 3 = 7 and x - 3 = -7.

Front

What is the solution to the inequality |x| < 4?

Back

-4 < x < 4.

Front

What is the solution to the inequality |x| > 2?

Back

x < -2 or x > 2.

Front

Evaluate the expression: |2 - 6|

Back

4.

Front

What does the compound inequality |x| ≤ 3 mean?

Back

It means that x is between -3 and 3, inclusive.

Front

What is the solution to the equation |x + 1| = 0?

Back

x = -1.

Front

Evaluate the expression: | -3 + 5 |

Back

2.

Front

What is the difference between 'and' and 'or' in compound inequalities involving absolute values?

Back

'And' means both conditions must be true, while 'or' means at least one condition must be true.