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 + 4| < 5?

Back

To solve |x + 4| < 5, split it into two inequalities: -5 < x + 4 < 5. This simplifies to -9 < x < 1.

Front

What does the solution -9 < x < 1 represent?

Back

It represents all values of x that are greater than -9 and less than 1.

Front

How do you solve the inequality |x - 4| ≥ 8?

Back

To solve |x - 4| ≥ 8, split it into two inequalities: x - 4 ≤ -8 or x - 4 ≥ 8. This gives x ≤ -4 or x ≥ 12.

Front

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

Back

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

Front

How do you solve the inequality |4x - 2| < 22?

Back

To solve |4x - 2| < 22, split it into two inequalities: -22 < 4x - 2 < 22. This simplifies to -5 < x < 6.

Front

What does the solution -5 < x < 6 represent?

Back

It represents all values of x that are greater than -5 and less than 6.

Front

How do you solve the inequality |x - 1| ≤ 6?

Back

To solve |x - 1| ≤ 6, split it into two inequalities: -6 ≤ x - 1 ≤ 6. This simplifies to -5 ≤ x ≤ 7.

Front

What does the solution -5 ≤ x ≤ 7 represent?

Back

It represents all values of x that are between -5 and 7, inclusive.

Front

How do you solve the inequality |x + 3| ≥ 10?

Back

To solve |x + 3| ≥ 10, split it into two inequalities: x + 3 ≤ -10 or x + 3 ≥ 10. This gives x ≤ -13 or x ≥ 7.