Absolute Value Inequality Special Cases

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

What does it mean when an absolute value expression is set equal to a negative number?

Back

An absolute value expression set equal to a negative number has no solution, as absolute values cannot be negative.

Front

Solve: |x| = 0

Back

x = 0

Front

What is the solution to |x - 3| = 5?

Back

x = 8 or x = -2

Front

What does the inequality |x| < a (where a > 0) represent?

Back

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

Front

What does the inequality |x| > a (where a > 0) represent?

Back

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

Front

Solve: |2x + 1| < 3

Back

-2 < 2x + 1 < 2, which simplifies to -3 < 2x < 1, giving x > -1.5 and x < 0.5.

Front

What is the solution to |x + 4| > 6?

Back

x < -10 or x > 2

Front

Solve: 3|x - 1| + 2 = 11

Back

x = 4 or x = -2.

Front

What is the result of solving |x - 2| = -3?

Back

no solution.