SOLUTION: Please help me solve this equation.. 3|-8x-9|=117

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Question 275281: Please help me solve this equation.. 3|-8x-9|=117
Found 2 solutions by jim_thompson5910, dabanfield:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3%2Aabs%28-8x-9%29=117 Start with the given equation


abs%28-8x-9%29=39 Divide both sides by 3



Break up the absolute value (remember, if you have abs%28x%29=a, then x=-a or x=a)

-8x-9=-39 or -8x-9=39 Set the expression -8x-9 equal to the original value 39 and it's opposite -39




Now lets focus on the first equation -8x-9=-39


-8x=-39%2B9Add 9 to both sides


-8x=-30 Combine like terms on the right side


x=%28-30%29%2F%28-8%29 Divide both sides by -8 to isolate x



x=15%2F4 Reduce






Now lets focus on the second equation -8x-9=39



-8x=39%2B9Add 9 to both sides


-8x=48 Combine like terms on the right side


x=%2848%29%2F%28-8%29 Divide both sides by -8 to isolate x



x=-6 Divide





So the solutions to 3%2Aabs%28-8x-9%29=117 are:

x=15%2F4 and x=-6

Answer by dabanfield(803) About Me  (Show Source):
You can put this solution on YOUR website!
3|-8x-9|=117
We have two cases. First when -8x-9 >= 0 the equation above becomes:
3*(-8x-9) = 117
-24x - 27 = 117
-24x = 90
x = -90/24 = -15/4 when
-8x - 9 >= 0
8x <= -9
x <= -9/8
In the second case when -8x-9 < 0 the original equation becomes:
3*-(-8x-9) = 117
3*(8x+9) = 117
24x + 27 = 117
24x = 90
x = 90/24 = 15/4 when
-8x-9 < 0
-8x < 9
x > 9/-8
x > -9/8
The solution set is {15/4, -15/4}