Question

How do you solve and graph `abs(x+8)<5`?

Answer 1

Write two equations one with the absolute value brackets being positive and one with the value being negative solve and graph.

Explanation:

an absolute value is the distance to zero. The value can be either the positive or negative but the distance to zero is the same.
So the inequality must be solved for both the positive and the negative values.

`+1( x +8) < 5` gives

`x + 8 < 5` Subtract 8 from both sides to find x gives

`x + 8 -8 < 5 -8` resulting in

`x < -3` make an empty circle at -3 and draw an arrow pointing to the left .

`-1 ( x + 8 ) < 5` gives

`-1x -8 < 5` Add 8 to both sides to isolate x gives

`-1x -8 +8 < 5 +8` Results in

`-1 x < 13` Now divide all three terms by -1
D
`-1x/ -1 = +x`

dividing < by -1 = > ( the opposite of < is >

`+13/-1 = -13` so

# x > -13 draw and empty circle at -13 and draw an arrow to the right.

The answer is the part of the line between -13 and -3.