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 \(x = 4\).
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