To know which equation has x= 8 as its only solution, we will need to solve for x in each equation:
3(2x + 1) + 5 = 4x + 2x + 8
open the parenthesis
6x + 3 + 5 = 6x + 8
6x + 8 = 6x + 8
The above has infinitely many solution
Let's move on and check for the next:
2(x+3) = 1/2 (6x -4)
open the parenthesis
2x + 6 = 3x - 2
collect like term
2x - 3x = -2 -6
-x = -8
x = 8
This equation has 8 as its only solution
Let's move on to the next and solve
-3x + 8 = x- 3x + 6 - 1/2(2x-4)
-3x + 8 = -2x + 6 - 1/2(2x - 4)
open the parenthesis
-3x + 8 = -2x + 6 - x + 2
-3x + 8 = -3x + 8
This equation has infinitely many solutions
Let's move on and solve for x in the next equation:
-(6x + 4) = 2x - 4
open the parenthesis
-6x - 4 = 2x - 4
collect like term
-8x = 0
x=0
Hence; the equation that has x = 8 as its only solution is;
2(x+3) = 1/2 (6x -4)