To solve the equation \( 5x - 12 - 6x = -10x + 7 - 1 \), we can follow these steps:
Step 1: Combine like terms on both sides.
On the left side:
- Combine \( 5x \) and \( -6x \): \[ 5x - 6x = -1x \quad \text{(or just } -x\text{)} \]
- So the left side becomes: \[ -x - 12 \]
On the right side:
- Simplify \( 7 - 1 \): \[ 7 - 1 = 6 \]
- So the right side becomes: \[ -10x + 6 \]
Now the equation looks like this: \[ -x - 12 = -10x + 6 \]
Step 2: Add \( 10x \) to both sides to isolate terms containing \( x \).
\[ -x + 10x - 12 = 6 \] This simplifies to: \[ 9x - 12 = 6 \]
Step 3: Add 12 to both sides to isolate the \( x \) term.
\[ 9x - 12 + 12 = 6 + 12 \] This simplifies to: \[ 9x = 18 \]
Step 4: Divide both sides by 9 to solve for \( x \).
\[ x = \frac{18}{9} \] This simplifies to: \[ x = 2 \]
Thus, the final solution is: \[ x = 2 \]
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