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

1 Answer
Oct 16, 2016

Answer:

#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())#