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

1 Answer
Aug 3, 2016

Answer:

#x in [5, 18]#

Explanation:

The first thing to do here is get #x# alone in the middle of the compound inequality by adding #7# to all three sides

#-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 #x# must satisfy 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 #x# to be greater than or equal to #5#. In interval notation, this is written as

#x in [5, +oo)#

For the second condition, you need #x# to be smaller than or equal to #18#. In interval notation, this is written as

#x in (-oo, 18]#

This means that the solution interval for the compound inequality must have #x# greater than or equal to #5# and smaller than or equal to #18#.

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)|)))#