Let's solve the equation \( 6x - 5x + 2 = 12 - 19 \).
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First, simplify both sides of the equation.
On the left side: \[ 6x - 5x + 2 = (6 - 5)x + 2 = 1x + 2 = x + 2 \]
On the right side: \[ 12 - 19 = -7 \]
So the equation becomes: \[ x + 2 = -7 \]
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Now, isolate \( x \) by subtracting 2 from both sides: \[ x = -7 - 2 \] \[ x = -9 \]
Now, let's check the solution by substituting \( x = -9 \) back into the original equation:
Original equation: \[ 6x - 5x + 2 = 12 - 19 \]
Substituting \( x = -9 \): \[ 6(-9) - 5(-9) + 2 = 12 - 19 \]
Calculating the left side: \[ 6(-9) = -54 \] \[ -5(-9) = 45 \] Now summarize: \[ -54 + 45 + 2 = -54 + 47 = -7 \]
Calculating the right side: \[ 12 - 19 = -7 \]
Since both sides equal \(-7\), our solution \( x = -9 \) is correct.
Thus, the final answer is: \[ \boxed{-9} \]