Question

solve for w.
7w + 23 = 4w + 8w - 22
simplify your answer as much as possible.

Explanation:

Step1: Combine like - terms on the right side

Combine $4w$ and $8w$ on the right side of the equation. The right - hand side becomes $4w + 8w-22=12w - 22$. So the equation is $7w + 23=12w-22$.

Step2: Move the terms with $w$ to one side

Subtract $7w$ from both sides of the equation:
$7w + 23-7w=12w-22-7w$.
This simplifies to $23 = 5w-22$.

Step3: Isolate the term with $w$

Add 22 to both sides of the equation:
$23 + 22=5w-22 + 22$.
We get $45 = 5w$.

Step4: Solve for $w$

Divide both sides of the equation by 5:
$\frac{45}{5}=\frac{5w}{5}$.
So $w = 9$.

Answer:

$9$