Simplify: |5x-1|=|3x+7|

5x-1 = 3x+7 => x = 4
or
5x-1 = -3x-7 => x = -3/4

|5x-1|=|3x+7|

Case 1:
5x-1 > 0 and 3x+7 > 0
5x-1 = 3x+7
2x=8
x=4
plug x=4 and verify the equation
|19| = |19|
satisfies the equation

Case 2:
5x-1 > 0 ; 3x+7 < 0
|5x-1| = 5x-1
|3x+7| = -(3x+7)

5x-1 = -3x-7
8x=-6
x=-6/8 = -3/4 --- satisfies the equation

Case 3:

5x-1 < 0 and 3x+7 > 0
|5x-1| = -(5x-1)
|3x+7| = 3x+7
-5x+1 = 3x+7
-8x = 6
x= -6/8 = -3/4
plug x=-3/4 and verify the equation
|-15/4-1| = |-9/4+7|
|-19/4| = |19/4| --- satisfies the equation

Case 4:
5x-1 < 0 and 3x+7 < 0
|5x-1| = -(5x-1)
|3x+7|= -(3x+7)
-5x+1 = -3x-7
-2x= -6
x=3
x=3 does not satisfy the equation
|14| = |16|

x=4,-3/4

5x=3x+6 simplifies to 2x= 6 which becomes x=3

|5x - 1| = |3x + 7|

3x + 7 = -(5x - 1)

3x + 7 = 5x - 1

8x = -6 --> x = -3/4

2x = 8 --> x = 4

(5x-1)=(3x+7)
5x-3x=1+7
2x=8
x=4

What on earth are those lines??

Anywhoo, your answer is probably x = 4