Question

(\frac{1}{2}(-10x + 4) = -4(-3 + 2x) + 8)

Explanation:

Step1: Distribute the coefficients

First, distribute $\frac{1}{2}$ on the left side and $-4$ on the right side.
For the left side: $\frac{1}{2}(-10x + 4)=\frac{1}{2}\times(-10x)+\frac{1}{2}\times4=-5x + 2$.
For the right side: $-4(-3 + 2x)+8=(-4)\times(-3)+(-4)\times(2x)+8 = 12-8x + 8$.
Simplify the right side: $12 + 8-8x=20-8x$.
So the equation becomes: $-5x + 2=20-8x$.

Step2: Move the variable terms to one side

Add $8x$ to both sides to get the $x$ terms on the left.
$-5x+8x + 2=20-8x+8x$.
Simplify: $3x + 2=20$.

Step3: Solve for x

Subtract 2 from both sides: $3x+2 - 2=20 - 2$.
Simplify: $3x=18$.
Divide both sides by 3: $\frac{3x}{3}=\frac{18}{3}$.
Simplify: $x = 6$.

Answer:

$x = 6$