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

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

Start with the given equation

Divide both sides by 3

Break up the absolute value (remember, if you have , then or )

or Set the expression equal to the original value 39 and it's opposite -39

Now lets focus on the first equation

Add 9 to both sides

Combine like terms on the right side

Divide both sides by -8 to isolate x

Reduce

Now lets focus on the second equation

Add 9 to both sides

Combine like terms on the right side

Divide both sides by -8 to isolate x

Divide

So the solutions to are:

and

Answer by dabanfield(803) (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}
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