Exercise 88 Page 48

Therefore, the absolute value inequality |x|>a is equivalent to the compound inequality x>a or x<- a. |x|> a ⇕ x> a or x<- a Now we can write the given absolute value inequalities as a compound inequality without an absolute value symbol.

The solution set of the inequality |x+3|< 4 includes all values whose distance from - 3 in the number line is less than 4, whereas that of the inequality |x+3| >4 includes all values whose distance from - 3 in the number line is greater than 4.

Extra

Solution Sets and Graphs

Solving each of the given inequalities is equivalent to solving its compound inequality.

Absolute Value Inequality	Compound Inequality	Solution Set
|x+3|<4	x+3<4 and x+3>- 4	x<1 and x >- 7
|x+3|>4	x+3>4 or x+3<- 4	x>1 or x<- 7

The graph of the inequality |x+3|<4 includes all values less than 1 and greater than - 7.

The graph of the inequality |x+3|>4 includes all values greater than 1 and less than - 7.