Alg 1 2.7: Absolute Value 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

What does the inequality |x| > a represent?

Back

It represents all values of x that are either greater than a or less than -a.

Front

What does the inequality |x| < a represent?

Back

It represents all values of x that are between -a and a.

Front

What is the solution to |x + 3| > -8?

Back

All real numbers.

Front

What is the solution to |2x - 12| + 8 = 8?

Back

x = 6.

Front

What is the solution to |2x - 1| = -7?

Back

No solution.

Front

What is the solution to 3 |2x + 7| + 7 < 4?

Back

No solution.

Front

What is the solution to -5|x - 4| < 20?

Back

All real numbers.

Front

How do you solve an absolute value inequality?

Back

Isolate the absolute value expression and then split it into two separate inequalities.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary points, while non-strict inequalities (≤, ≥) do include them.