Sure, let's solve the equation step by step.
The given equation is:
[tex]\[ 8(x-1) = -4x + 136 \][/tex]
1. Distribute the 8 on the left side:
[tex]\[ 8 \cdot x - 8 \cdot 1 = 8x - 8 \][/tex]
[tex]\[ 8x - 8 = -4x + 136 \][/tex]
2. Move all terms involving [tex]\( x \)[/tex] to one side and constants to the other side. Add [tex]\( 4x \)[/tex] to both sides:
[tex]\[ 8x + 4x - 8 = 136 \][/tex]
This simplifies to:
[tex]\[ 12x - 8 = 136 \][/tex]
3. Add 8 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 12x - 8 + 8 = 136 + 8 \][/tex]
This simplifies to:
[tex]\[ 12x = 144 \][/tex]
4. Divide both sides by 12 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{144}{12} \][/tex]
[tex]\[ x = 12 \][/tex]
So, the solution for [tex]\(x\)[/tex] is [tex]\( \boxed{12} \)[/tex].
