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

What does the inequality |x| < a represent?

Back

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

Front

What does the inequality |x| > a represent?

Back

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

Front

What is the solution to the equation |x| = a?

Back

The solutions are x = a and x = -a.

Front

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

Back

'And' is used when both conditions must be true (intersection), while 'or' is used when at least one condition must be true (union).

Front

Solve the absolute value equation |x - 3| = 5.

Back

x = 8 or x = -2.

Front

Solve the absolute value inequality |x + 4| < 3.

Back

-7 < x < -1.

Front

What is the solution set for |2x - 4| ≥ 6?

Back

x ≤ -1 or x ≥ 5.

Front

How do you graph the inequality |x| < 2?

Back

Graph the interval (-2, 2) on the number line.

Front

What is the solution to the equation |3x + 1| = 0?

Back

x = -1/3.