To solve the equation \( 2x - 5(x - 4) = -2 + 3x + 10 \), let's simplify both sides step by step.
Step 1: Simplify the left side
Starting with the left-hand side: \[ 2x - 5(x - 4) \] Distributing \(-5\): \[ 2x - 5x + 20 \] Combining like terms: \[ -3x + 20 \]
Step 2: Simplify the right side
Now simplifying the right-hand side: \[ -2 + 3x + 10 \] Combine the constants: \[ 3x + 8 \]
Step 3: Set the equation
Now we have the simplified equation: \[ -3x + 20 = 3x + 8 \]
Step 4: Solve for \( x \)
Add \( 3x \) to both sides: \[ 20 = 6x + 8 \] Next, subtract \( 8 \) from both sides: \[ 12 = 6x \] Now divide by \( 6 \): \[ x = 2 \]
Conclusion
The value of \( x \) is: \[ \boxed{2} \]
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