Question

Consider this equation:

–2x – 4 + 5x = 8

Generate a plan to solve for the variable. Describe the steps that will be used.

Answer 1

To solve the equation \(-2x - 4 + 5x = 8\), we can follow these steps:

### Step 1: Combine like terms on the left side
- Start by combining the \(x\) terms. We have \(-2x\) and \(5x\).
- \(-2x + 5x = 3x\)
- Rewrite the equation with the combined terms:
\[
3x - 4 = 8
\]

### Step 2: Isolate the term with the variable
- Next, we want to get \(3x\) by itself on one side of the equation. To do this, we need to eliminate \(-4\) from the left side.
- Add \(4\) to both sides of the equation:
\[
3x - 4 + 4 = 8 + 4
\]
- Simplifying this gives us:
\[
3x = 12
\]

### Step 3: Solve for the variable
- Now we need to solve for \(x\) by isolating it. To do this, divide both sides of the equation by \(3\):
\[
\frac{3x}{3} = \frac{12}{3}
\]
- This simplifies to:
\[
x = 4
\]

### Step 4: Verify the solution
- To ensure our solution is correct, we can substitute \(x = 4\) back into the original equation:
\[
-2(4) - 4 + 5(4) = 8
\]
\[
-8 - 4 + 20 = 8
\]
\[
8 = 8
\]
- Since both sides of the equation are equal, our solution \(x = 4\) is correct.

### Conclusion
- The value of \(x\) that satisfies the equation \(-2x - 4 + 5x = 8\) is \(x = 4\).