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

2 Answers
Apr 25, 2017

See the entire solution process below:

Explanation:

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]

Apr 25, 2017

-13<=x< 7

Explanation:

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