3.7.4 Special Solutions with Absolute value Inequalities

Front

What does the inequality |2x - 1| ≥ -1 imply?

Back

All Real Numbers

Front

Is the inequality |x - 2| > 3 an 'and' or an 'or' problem?

Back

or

Front

What is the first step to solve |x - 5| = 10?

Back

Get the absolute value alone by subtracting 5 from both sides.

Front

What does the inequality |5 + 6x| > -5 imply?

Back

Infinite Solutions

Front

What is the correct first step to solve |10x| = 20?

Back

Multiply by 10.

Front

What is the definition of an absolute value inequality?

Back

An inequality that contains an absolute value expression, representing the distance of a number from zero.

Front

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

Back

Create two inequalities: x - a < b and x - a > -b.

Front

What is the solution set for |x| < c where c > 0?

Back

(-c, c) in interval notation.

Front

What is the solution set for |x| > c where c > 0?

Back

(-∞, -c) ∪ (c, ∞) in interval notation.

Front

What is the first step in solving |x + 3| ≤ 4?

Back

Create two inequalities: x + 3 ≤ 4 and x + 3 ≥ -4.