Question

6 |6-4x|=8x+4 solve please need work shown

Answer 1

First, since there is an absolute value in the equation you must split it into two equations: 6(6x+4)=8x+4 and 6(6x-4)=8x+4

Answer 2

Solving the first: 36x+24=8x+4
28x-28=0
28x=28
and x=1

Answer 3

Then 36x+24=8x+4
36x+20=8x
28x+20=0
28x=-20
x=(-28/20)

Answer 4

If |A| = B it implies A = B or A = -B
6 |6x-4|=8x+4
|36x - 24| = 8x + 4
Split it into two equations to get rid of the absolute bars:
36x - 24 = 8x + 4 or 36x - 24 = -(8x + 4) 36x - 24 = -8x - 4
add -8x: or add 8x
28x - 24 = 4 or 44x - 24 = -4
add 24: or add 24
28x = 28 or 44x = 20
divide by 28 or divide by 44
x = 1 or x = 20/44 = 5/11

x = 5/11, 1

Answer 5

http://www.wolframalpha.com/input/?i=6+%7C6-4x%7C%3D8x%2B4
\[6 \left| 6-4x \right|=8x+4\]\[\implies \left| 36-24x \right|=8x+4\]we can divide both sides by 4:\[\implies \left| 9-6x \right|=2x+1\]

Answer 6

Oh, I copied the question wrong from the very first reply rather than from the original problem.

Answer 7

\[\begin{matrix}{9-6x=2x+1\\ \implies8x=8\\ \implies x=1} & ,or &{9-6x=-2x-1\\ \implies4x=10\\ \implies x=\frac52 }\end{matrix}\]