Absolute Value Equations

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 like |x| = a?

Back

To solve |x| = a, you set up two equations: x = a and x = -a.

Front

What does the inequality |x| < a represent?

Back

The inequality |x| < a means that x is within a distance of a from zero, or -a < x < a.

Front

What does the inequality |x| > a represent?

Back

The inequality |x| > a means that x is outside the distance of a from zero, or x < -a or x > a.

Front

Solve the inequality |x - 4| < 3.

Back

1 < x < 7.

Front

Solve the inequality |2x + 1| > 5.

Back

x < -3 or x > 2.

Front

What is the solution to the inequality |x + 2| ≤ 4?

Back

-6 ≤ x ≤ 2.

Front

How do you graph the inequality |x| < 3?

Back

Draw a number line and shade the region between -3 and 3, not including the endpoints.

Front

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

Back

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

Front

Solve the absolute value equation |3x - 1| = 5.

Back

x = 2 or x = -4/3.