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

Let's solve the equation step by step:

\[
7w - 2(w - 9) = 4 - 8(w + 2)
\]

### Step 1: Distribute the constants in parentheses
Distribute \(-2\) over \((w - 9)\) and \(-8\) over \((w + 2)\):

\[
7w - 2w + 18 = 4 - 8w - 16
\]

Simplify both sides:

\[
(7w - 2w) + 18 = (4 - 16) - 8w
\]

\[
5w + 18 = -12 - 8w
\]

### Step 2: Move all terms involving \(w\) to one side
Add \(8w\) to both sides:

\[
5w + 8w + 18 = -12
\]

\[
13w + 18 = -12
\]

### Step 3: Isolate \(w\)
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:

\[
w = \frac{-30}{13}
\]

Would you like more details or have any questions?

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Here are 5 related questions:
1. What is the general process to solve linear equations involving distribution?
2. How do you check if your solution to an equation is correct?
3. What happens if you have variables on both sides of an equation?
4. Can this type of equation have more than one solution?
5. What is the significance of fractions in linear equations?

**Tip:** Always simplify both sides of the equation before isolating the variable for easier calculation.

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

Discover how to solve the linear equation 7w−2(w−9)=4−8(w+2) using algebraic principles such as the distributive property and solving for a variable. This step-by-step guide simplifies the process, making it suitable for Grades 7-10.

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