# How do you solve #-2<=x-7<=11#?

##### 1 Answer

#### Explanation:

The first thing to do here is get **compound inequality** by adding

#-2 + 7 <= x - color(red)(cancel(color(black)(7))) <= 11 + 7#

#color(white)(aaaaa)5 <= color(white)(aa)xcolor(white)(aa) <= 18#

You now know that in order to be part of the solution interval, a value of **two conditions**

#x >= color(white)(1)5 -># the left side of the compound inequality

#x <= 18 -># the right side of the compound inequality

For the first condition, you need *greater than or equal to*

#x in [5, +oo)#

For the second condition, you need *smaller than or equal to*

#x in (-oo, 18]#

This means that the solution interval for the compound inequality must have * and* smaller than or equal to

Thsi is written as

#x in (-oo, 18] nn [5, +oo) implies color(green)(|bar(ul(color(white)(a/a)color(black)( x in [5, 18])color(white)(a/a)|)))#