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 \(-2x - 4 + 5x = 8\), you can follow this step-by-step plan:

### Step 1: Combine like terms
Combine the \(x\) terms on the left side of the equation. You have \(-2x\) and \(5x\) which can be combined:

\[
-2x + 5x = 3x
\]

### Step 2: Rewrite the equation
After combining the like terms, rewrite the equation:

\[
3x - 4 = 8
\]

### Step 3: Isolate the term with the variable
To isolate the term with the variable (\(3x\)), add \(4\) to both sides of the equation:

\[
3x - 4 + 4 = 8 + 4
\]

This simplifies to:

\[
3x = 12
\]

### Step 4: Solve for the variable
Now, divide both sides of the equation by \(3\) to solve for \(x\):

\[
x = \frac{12}{3}
\]

This simplifies to:

\[
x = 4
\]

### Step 5: Verify the solution
To ensure the solution is correct, substitute \(x = 4\) back into the original equation:

\[
-2(4) - 4 + 5(4) = 8
\]

Calculating the left side:

\[
-8 - 4 + 20 = 8
\]
\[
8 = 8
\]

Since both sides are equal, the solution \(x = 4\) is verified.

### Summary
- Combine like terms to simplify the equation.
- Isolate the variable by adding or subtracting constant terms.
- Solve for the variable by dividing or multiplying by coefficients.
- Verify the solution by substituting it back into the original equation.

So, the final answer is \(x = 4\).