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 inequality |2x + 5| > 11 represent?

Back

It represents two separate inequalities: 2x + 5 > 11 or 2x + 5 < -11.

Front

How do you isolate x in the equation |x - 3| = 7?

Back

You set up two equations: x - 3 = 7 and x - 3 = -7, then solve for x.

Front

What is the first step in solving |2x + 12| < 8?

Back

The first step is to set up the two inequalities: 2x + 12 < 8 and 2x + 12 > -8.

Front

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

Back

The solution is -5 < w < 6.

Front

How do you graph the solution of |x| < a on a number line?

Back

You draw an open interval between -a and a, indicating all numbers between these two points.

Front

What is the difference between |x| < a and |x| > a?

Back

|x| < a means x is within a distance a from 0, while |x| > a means x is outside that distance.

Front

What is the solution to the inequality |x + 4| > 3?

Back

The solution is x < -7 or x > -1.