Absolute Value Inequalities

Front

What is an absolute value inequality?

Back

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

Front

How do you solve the inequality |x - a| < b?

Back

To solve |x - a| < b, you split it into two inequalities: a - b < x < a + b.

Front

How do you solve the inequality |x - a| > b?

Back

To solve |x - a| > b, you split it into two inequalities: x < a - b or x > a + b.

Front

What does the solution x < 1 and x > -14 represent?

Back

It represents the range of values for x that are between -14 and 1, not including -14 and 1.

Front

What does the solution x > 5 or x < -11 represent?

Back

It represents the values of x that are either greater than 5 or less than -11.

Front

What does the solution y ≤ -4 or y ≥ 12 represent?

Back

It represents the values of y that are either less than or equal to -4 or greater than or equal to 12.

Front

How do you graph the solution of an absolute value inequality?

Back

You graph the critical points found from solving the inequality and shade the appropriate regions based on the type of inequality (and/or).

Front

What is the difference between 'and' and 'or' in absolute value inequalities?

Back

'And' indicates a range of values between two points, while 'or' indicates values that fall outside of two points.

Front

Solve the inequality |2x + 13| < 15.

Back

x < 1 and x > -14.

Front

Solve the inequality |10 + 4x| < 14.

Back

x < 1 and x > -6.