Question

solve for z.
-7 + 3z = -2z + 5 + 8z
z =

Explanation:

Step1: Combine like - terms on right side

Combine the $z$ terms on the right side of the equation $-7 + 3z=-2z + 5+8z$. The right - hand side simplifies to $(-2z + 8z)+5=6z + 5$. So the equation becomes $-7 + 3z=6z + 5$.

Step2: Move $z$ terms to one side

Subtract $3z$ from both sides of the equation: $-7+3z-3z=6z + 5-3z$. This simplifies to $-7 = 3z+5$.

Step3: Move constant terms to one side

Subtract 5 from both sides: $-7-5=3z+5 - 5$. So, $-12 = 3z$.

Step4: Solve for $z$

Divide both sides by 3: $\frac{-12}{3}=\frac{3z}{3}$. Thus, $z=-4$.

Answer:

$-4$