How do you solve the inequality #-5<=x+8<15#?

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Answer 1 · 2017-04-25T02:15:41

See the entire solution process below:

Subtract #color(red)(8)# from each segment of the system of inequalities to solve for #x# while keeping the system balanced:

#-5 - color(red)(8) <= x + 8 - color(red)(8) < 15 - color(red)(8)#

#-13 <= x + 0 < 7#

#-13 <= x < 7#

Or

#x >= -13# and #x < 7#

Or, in interval form:

#(-13, 7]#

Answer 2 · 2017-04-25T02:30:34

-13#<=#x#<# 7

There are two ways to do this.

The first way is to separate the inequalities and go from there,

Given:
-5#<=#x + 8#<# 15

Separated:
-5#<=#x + 8 , and x + 8#<#15

Then simply solve for x by subtracting 8:
-13#<=#x , and x#<#7

Finally combine to get:
-13#<=#x#<# 7

The second method to solve this is to do it together,

Given:
-5#<=#x + 8#<# 15

Subtract 8 from both sides and get the answer:
-13#<=#x#<# 7