How to solve this? basic algebra.?

x = 11

x=11

x=11

:))

1/4x-1/4=(x+4)/6

open the brackets on the rightside
=>1/4x-1/4=x/6+4/6

bring the x terms to oneside
=>1/4x-x/6=1/4+4/6

cross multiplication
=>(6-4xx)/24x=(6+4)/24

multiply 24 on both sides
=>(6-4xx)/x=10
=>6-4xx=10x
=>4xx+10x-6=0
splitting the middle term(sum=10 and product= -4*6=-24 factors of are 24 are 2*2*2*3
using 2,2,2,3 sum should be+10 and product -24 possible with the combination (2*2*3)-2 that is 12-2)

=>4xx+12x-2x-6=0
=>4x(x+3)-2(x+3)=0

taking the common term (x+3)
=>(x+3)(4x-2)=0

=>(x+3)=0 or (4x-2)=0
=>x=-3 or 4x=2
=> x=-3 or x=1/2

Should be written as :-
(1/4) x - 1/4 = (x + 4) / 6
3x - 3 = 2x + 8
x = 11

Note
1 / 4x and (1/4) x are not the same thing.

get x terms on 1 side

x-1=4x/6 + 16/6
6x-6=4x+16

6x-4x=16+6

2x=22
x=11

1/4(x) - 1/4 = (x + 4)/6
x/4 - 1/4 = (x + 4)/6
12(x/4 - 1/4) = 12(x + 4)/6
3x - 3 = 2(x + 4)
3x - 3 = 2*x + 2*4
3x - 2x = 3 + 8
x = 11

x = 11.

Multiply both sides by 6.
Move x's to the same side.
Move everything else over.
Multiply through by the inverse of the coefficient of x.

x = 11

clear fractions multiply everything by 12

3x - 3 = 2 ( x + 4)

3x - 3 = 2x + 8

x - 3 = 8

x = 11