How do you solve #-10| h + 5| - 3= - 83#?
1 Answer
Explanation:
Your first goal here is to isolate the modulus on one side of the equation. To do that, add
#-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())#
