SOLUTION: I have to solve the equation below. It is a multiple choice question so I also listed them below. Equation: 1/6 the absolute value of 4x-8 = 6x Multiple choice answers: A x

Algebra ->  Absolute-value -> SOLUTION: I have to solve the equation below. It is a multiple choice question so I also listed them below. Equation: 1/6 the absolute value of 4x-8 = 6x Multiple choice answers: A x      Log On


   

Question 333582: I have to solve the equation below. It is a multiple choice question so I also listed them below.
Equation: 1/6 the absolute value of 4x-8 = 6x
Multiple choice answers: A x=8/3, x=8/5 B no solution C x=1/5 D x=-7, x=11
First I multiplied both sides by 6 to eliminate the 1/6 on the right side and made the left side 36x. Then I split the equation into 2 so that the first equation was:4x-8=36x and the second one was 4x-8=-36x. Next, on the first problem, I subtracted 4x from both sides so it was -8=32x, then I divided both sides by 32 to isolate x and got -8/32=x which I simplified into x=-1/4. On the second problem I added 8 to both sides and subtracted 36x from both sides to get 40x=8. Then, I divided both sides by 40 to isolate x and got x=8/40 or x=1/5. My question is: which answer should I choose and is my algebra correct or did I make a mistake?
Thank you!!!
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F6abs%284x-8%29%22%22=%22%226x

abs%284x-8%29%22%22=%22%2236x

4x-8%22%22=%22%2236x;  4x-8%22%22=%22%22-36x

-8%22%22=%22%2232x;  -8%22%22=%22%22-40x

-8%2F32%22%22=%22%22x;  -8%2F%28-40%29%22%22=%22%22x

-1%2F4%22%22=%22%22x;  1%2F5%22%22=%22%22x  

Therefore your work is correct.

To find out if these are solutions substitute them into the 
original equation.

Substituting x=-1%2F4 in the original

1%2F6abs%284x-8%29%22%22=%22%226x

1%2F6abs%284%28-1%2F4%29-8%29%22%22=%22%226%28-1%2F4%29

1%2F6abs%28-1-8%29%22%22=%22%22-6%2F4

1%2F6abs%28-9%29%22%22=%22%22-3%2F2

1%2F6%289%29%22%22=%22%22-3%2F2

9%2F6%22%22=%22%22-3%2F2

3%2F2%22%22=%22%22-3%2F2

Certainly that's false, so -1%2F4 is an extraneous solution,

which we discard.

Substituting x=1%2F5 in the original

1%2F6abs%284x-8%29%22%22=%22%226x

1%2F6abs%284%281%2F5%29-8%29%22%22=%22%226%281%2F5%29

1%2F6abs%284%2F5-8%29%22%22=%22%226%2F5

1%2F6abs%284%2F5-40%2F5%29%22%22=%22%226%2F5

1%2F6abs%28-36%2F5%29%22%22=%22%226%2F5

1%2F6%2836%2F5%29%22%22=%22%226%2F5

6%2F5%22%22=%22%226%2F5

That one checks, so the only solution is x=1%2F5

Edwin