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

How do you solve the inequality |x + 3| > 8?

Back

Separate into two inequalities: x + 3 > 8 or x + 3 < -8, leading to x > 5 or x < -11.

Front

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

Back

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

Front

What is the first step in solving | -8x | < 8?

Back

Separate into two inequalities with an 'and': -8x < 8 and -8x > -8.

Front

What is the solution to the inequality |x| < a?

Back

The solution is -a < x < a.

Front

What does the compound inequality m < -1 OR m > 2 indicate?

Back

It indicates that m can take any value less than -1 or any value greater than 2.

Front

How do you represent the solution n > 10 or n < -6 graphically?

Back

On a number line, shade the region to the right of 10 and the region to the left of -6.

Front

What is the difference between 'and' and 'or' in compound inequalities?

Back

'And' means both conditions must be true simultaneously, while 'or' means at least one condition must be true.

Front

How do you solve |x - 4| ≤ 3?

Back

Separate into two inequalities: x - 4 ≤ 3 and x - 4 ≥ -3, leading to 1 ≤ x ≤ 7.

Front

What is the first step in solving |2x + 5| > 7?

Back

Separate into two inequalities: 2x + 5 > 7 or 2x + 5 < -7.