Explanation Please?

Sure

1/2 (x-5) = x/4   multiply both sides by 4 to clear the fractions

4(1/2) (x- 5)  = x/4 *(4)            [ x/4 =  (1/4)x .......so   4(1/4) x   = x ]

2 (x - 5)  = x        distribute the 2 across the terms in the parentheses on the left

2x - 10   =  x         subtract x from both sides

 -x             -x

x  - 10   =   0         add 10 to both sides

   + 10      + 10

x      =    10

Does that help???

x=10

OK, young person. Here is the solution step by step. Good luck.

Solve for x:
(x-5)/2 = x/4
Make (x-5)/2 = x/4 simpler by multiplying both sides by a constant.
Multiply both sides by 4:
(4 (x-5))/2 = (4 x)/4
In (4 (x-5))/2, divide 4 in the numerator by 2 in the denominator.
4/2 = (2×2)/2 = 2:
2 (x-5) = (4 x)/4
Cancel common terms in the numerator and denominator of (4 x)/4.
(4 x)/4 = 4/4×x = x:
2 (x-5) = x
Write the linear polynomial on the left hand side in standard form.
Expand out terms of the left hand side:
2 x-10 = x
Move terms with x to the left hand side.
Subtract x from both sides:
(2 x-x)-10 = x-x
Combine like terms in 2 x-x.
2 x-x = x:
x-10 = x-x
Look for two terms that sum to zero.
x-x = 0:
x-10 = 0
Isolate terms with x to the left hand side.
Add 10 to both sides:
x+(10-10) = 10
Look for two terms that sum to zero.
10-10 = 0:
Answer: | 
| x = 10