Absolute Value Inequalities Review

Front

What is an absolute value inequality?

Back

An inequality that contains an absolute value expression, which measures the distance of a number from zero on the number line.

Front

What does the symbol |x| represent?

Back

The absolute value of x, which is the distance of x from 0 on the number line, always non-negative.

Front

When solving |x - a| < b, what type of compound inequality is formed?

Back

An 'and' compound inequality.

Front

When solving |x - a| > b, what type of compound inequality is formed?

Back

An 'or' compound inequality.

Front

What does the solution to |x - 2| < 3 look like on a number line?

Back

The solution is the interval (−1, 5), shaded between -1 and 5.

Front

What does the solution to |x - 2| > 3 look like on a number line?

Back

The solution is the union of the intervals (-∞, -1) and (5, ∞), shaded outside of -1 and 5.

Front

What is the first step in solving |2x| < 10?

Back

Divide both sides by 2 to get |x| < 5.

Front

What is the first step in solving |3x - 1| > 4?

Back

Set up two inequalities: 3x - 1 > 4 and 3x - 1 < -4.

Front

What does 'AND' mean in compound inequalities?

Back

Both conditions must be true for the solution to be valid.

Front

What does 'OR' mean in compound inequalities?

Back

At least one of the conditions must be true for the solution to be valid.