Question

How do you solve `-10| h + 5| - 3= - 83`?

Answer 1

`h in {-13, 3}`

Explanation:

Your first goal here is to isolate the modulus on one side of the equation. To do that, add `3` to both sides and divide both sides by `-10`

`-10 * |h + 5| - color(red)(cancel(color(black)(3)))+ color(red)(cancel(color(black)(3))) = - 83 + 3`

`-10 * |h + 5| = - 80`

`(color(red)(cancel(color(black)(-10))) * |h+5|)/(color(red)(cancel(color(black)(-10)))) = (-80)/(-10)`

`|h + 5| = 8`

At this point, you have two possible cases to look at

• `h + 5 >= 0 implies |h + 5| = h + 5`

This gets you

`h + 5 = 8 implies h = 3`

• `h + 5 < 0 implies |h + 5| = -(h+5)`

This time, you have

`-(h + 5) = 8`

`-h - 5 = 8`

`h = -13`

Therefore, the original equation has two possible solutions

`h in {-13, 3}`

Do a quick double-check to make sure that the calculations are correct

`-10 * |3 + 5| - 3 = -83`

`-10 * 8 - 3 = - 83" "color(green)(sqrt())`

and

`-10 * |-13 + 5| - 3= - 83`

`-10 * |-8| - 3 = - 83`

`-10 * 8 - 3 = - 83" "color(green)(sqrt())`