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 \(x = 4\).
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