explain absolute value equation and inequalities with examples

Question

explain how to use absolute value equation and inequalities with examples in college algebra

Answer 1

Let's take the inequality |x + 2| > 5 . Since we're taking the absolute value of x+2, then x+2 could be positive or negative. Therefore, we need to consider both situations:

x + 2 > 5    or x + 2 < -5

WAIT! Why did the direction of the sign change???

We could also look at this as:

x + 2 > 5   or (-1)(x + 2) > 5  (the negative of x+2 is greater than 5) . In the second inequality, once we divide by (-1), the direction of the inequality changes. 

Now we solve each one separately:

x + 2 > 5    ===> x > 3

X + 2 < -5   ===> x < -7

so our solution set is x > 3 or x < -7

Why is it OR and not AND? Because our solutions go different directions on the number line, and both cannot be true at the same time.