Alg 2 - Review #2 - Solving Equations and Absolute Values

Front

What is the definition of an absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

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

Back

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

Front

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

Back

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

Front

What does the graph of |x| < a look like?

Back

The graph consists of a segment between -a and a on the number line.

Front

What does the graph of |x| > a look like?

Back

The graph consists of two rays extending from -a to the left and from a to the right on the number line.

Front

For the inequality |2x + 5| > 11, what is the first step to solve it?

Back

Set up two inequalities: 2x + 5 > 11 and 2x + 5 < -11.

Front

What is the solution to the inequality |2w - 1| < 11?

Back

The solution is -5 < w < 6.

Front

How do you isolate x in the equation |2x + 12| < 8?

Back

First, split it into two inequalities: 2x + 12 < 8 and 2x + 12 > -8.

Front

What is the first step in solving |x - 3| = 7?

Back

Set up two equations: x - 3 = 7 and x - 3 = -7.

Front

What is the solution to the equation |x + 4| = 10?

Back

The solutions are x = 6 and x = -14.