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

Let's solve the equation step by step:

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

### Step 1: Distribute the terms

1. On the left-hand side:
   \[
   7w - 2(w - 9) = 7w - 2w + 18
   \]
   Simplifying gives:
   \[
   5w + 18
   \]

2. On the right-hand side:
   \[
   4 - 8(w + 2) = 4 - 8w - 16
   \]
   Simplifying gives:
   \[
   -8w - 12
   \]

So now we have:
\[
5w + 18 = -8w - 12
\]

### Step 2: Combine like terms

To move all terms involving \(w\) to one side, add \(8w\) to both sides:
\[
5w + 8w + 18 = -12
\]
This simplifies to:
\[
13w + 18 = -12
\]

### Step 3: Isolate the variable

Now, subtract 18 from both sides:
\[
13w = -12 - 18
\]
\[
13w = -30
\]

### Step 4: Solve for \(w\)

Finally, divide both sides by 13:
\[
w = \frac{-30}{13}
\]

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

Let me know if you want any further details or have any questions.

### Related questions:
1. How do you handle equations with variables on both sides?
2. What is the distributive property and how is it used in algebra?
3. How do you solve for a variable when it is in a fraction?
4. How can you check your solution to an algebraic equation?
5. What is the significance of simplifying like terms in an equation?

**Tip:** Always perform operations step by step to avoid mistakes, especially when distributing and combining like terms.

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

Find out how to solve the linear equation 7w−2(w−9)=4−8(w+2) using key algebraic techniques such as the distributive property and combining like terms. This step-by-step guide is perfect for students in Grades 7-9 looking to strengthen their algebra skills.

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