What is the solution to the equation 7w−2(w−9)=4−8(w+2)7w−2(w−9)=4−8(w+2)?

A.w=−269w=−269

B.w=−109w=−109

C.w=1513w=1513

D.w=−3013w=−3013

Let's solve the equation step by step:

The given equation is:
\[
7w - 2(w - 9) = 4 - 8(w + 2)
\]

### Step 1: Expand both sides
First, expand the terms on both sides.

For the left-hand side:
\[
7w - 2(w - 9) = 7w - 2w + 18 = 5w + 18
\]

For the right-hand side:
\[
4 - 8(w + 2) = 4 - 8w - 16 = -8w - 12
\]

Now the equation becomes:
\[
5w + 18 = -8w - 12
\]

### Step 2: Move all \( w \)-terms to one side
Add \( 8w \) to both sides:
\[
5w + 8w + 18 = -12
\]
\[
13w + 18 = -12
\]

### Step 3: Isolate the \( w \)-term
Subtract 18 from both sides:
\[
13w = -12 - 18
\]
\[
13w = -30
\]

### Step 4: Solve for \( w \)
Divide both sides by 13:
\[
w = \frac{-30}{13}
\]

Thus, the solution is:
\[
w = \frac{-30}{13}
\]

### Conclusion:
The correct answer is:
\[
\boxed{D. \, w = \frac{-30}{13}}
\]

---

Would you like further details on any step or have any questions? Here are 5 related problems you might find useful:

1. Solve \( 3x - 5(x + 1) = 7 - 2(x - 4) \).
2. Solve \( 8y + 6 = 2(y + 4) - 3y \).
3. Solve \( 9 - 4(z + 2) = 2z + 6 \).
4. Solve \( 5(a - 2) + 3a = 4(2a + 1) - 7 \).
5. Solve \( 4b - 7(b + 3) = -2(3b + 1) \).

**Tip:** Always simplify and expand expressions carefully to avoid errors in solving equations.

What is the solution to the equation 7w−2(w−9)=4−8(w+2)? A. w=−269 B. w=−109 C. w=1513 D. w=−3013

Step-by-step guide to solving the linear equation 7w−2(w−9)=4−8(w+2). Learn how to simplify and isolate variables using algebraic techniques. This solution covers key concepts such as equation expansion, combining like terms, and isolating variables, suitable for students in Grades 7-9.

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