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

Front

What does the solution x < 1 and x > -6 represent?

Back

It represents the range of x values that are between -6 and 1, not including -6 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 is the graphical representation of |x - 3| < 5?

Back

The graph shows a line segment between -2 and 8 on the number line.

Front

What is the graphical representation of |y - 4| ≥ 8?

Back

The graph shows two rays extending from -4 to the left and from 12 to the right on the number line.

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 outside of a certain range.

Front

Solve the inequality |2x - 4| < 10.

Back

x is between -3 and 7, so -3 < x < 7.

Front

Solve the inequality |x + 3| ≥ 8.

Back

x ≤ -11 or x ≥ 5.