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 represents the distance of a number from zero on a number line.

Front

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

Back

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

Front

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

Back

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

Front

What does the inequality |4v + 12| ≥ 6 represent?

Back

It represents the values of v for which the expression 4v + 12 is at least 6 units away from 0.

Front

Solve the inequality |4v + 12| ≥ 6.

Back

v ≤ -4.5 or v ≥ -1.5.

Front

What does the inequality |2t + ⅔| < 4 represent?

Back

It represents the values of t for which the expression 2t + ⅔ is less than 4 units away from 0.

Front

Solve the inequality |2t + ⅔| < 4.

Back

-5/3 < t < 7/3.

Front

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

Back

The solution indicates the range of values that satisfy the inequality, often expressed as intervals.

Front

Solve the inequality |-3f| ≥ 6.3.

Back

f ≤ -2.1 or f ≥ 2.1.

Front

What is the significance of the number 213 in the context of the box of crackers?

Back

213g is the target weight for the boxes of crackers, and any box that deviates from this weight by more than 5g is considered unacceptable.