You have the following equation:
1) -4(x - 24) + 1/2(x + 4) = x + 15
in order to solve for x the previous equation, proceed as follow:
-4(x - 24) + 1/2(x + 4) = x + 15 multiply by 2 both sides
-8(x - 24) + (x + 4) = 2x + 30 apply distribution property
-8x + 192 + x + 4 = 2x + 30 simplify like terms both sides
-7x + 196 = 2x + 30 subtract 2x and subtract 196 bot sides
-7x - 2x = 30 - 196
-9x = -166 divide by -9 both sides
x = -166/(-9)
x = 18.44
2)
12(x + 2) - 4x = 4(2x + 11) - 20 apply distribution property
12x + 24 - 4x = 8x + 44 - 20
8x + 24 = 8x + 24
0 = 0
In this case, you have infinite solutions