Solving Absolute Value Inequalities

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

When should you write two expressions for an absolute value inequality?

Back

After isolating the absolute value symbol and determining 'and' or 'or' statement.

Front

What is the solution to the inequality |3x - 4| ≤ 17?

Back

x ≤ 7 and x ≥ -13/3.

Front

For the inequality |4x - 3| > -4, what is the solution?

Back

All real numbers.

Front

For the inequality |2x + 5| > 11, what is the solution?

Back

x > 3 or x < -8.

Front

What is the correct order of steps to solve an absolute value inequality?

Back

Isolating the absolute value symbol, determine 'and' or 'or' statement, write two expressions, solve each inequality.

Front

What does the symbol '|' represent in an absolute value inequality?

Back

It represents the absolute value, which indicates the distance from zero.

Front

How do you determine if you use 'and' or 'or' in absolute value inequalities?

Back

Use 'and' for 'less than' (< or ≤) and 'or' for 'greater than' (> or ≥).

Front

What is the solution set for |x| < a, where a > 0?

Back

-a < x < a.

Front

What is the solution set for |x| > a, where a > 0?

Back

x < -a or x > a.