Let's follow the steps to solve the equation \( 5x - 12 - 6x = -10x + 7 - 1 \).
Step 1: Combine like terms to get: On the left side, combine \( 5x \) and \(-6x\): \[ 5x - 6x = -x \]
On the right side, combine \( 7 \) and \(-1\): \[ 7 - 1 = 6 \]
So, the equation simplifies to: \[ -x - 12 = -10x + 6 \]
Response area: \(-x - 12 = -10x + 6\)
Step 2: Get the x-terms on the same side of the equation: Add \( 10x \) to both sides of the equation: \[ -x + 10x - 12 = 6 \]
This simplifies to: \[ 9x - 12 = 6 \]
Response area: \(9x - 12 = 6\)
Step 3: Get the constants on the same side of the equation: Add \( 12 \) to both sides of the equation: \[ 9x - 12 + 12 = 6 + 12 \]
This simplifies to: \[ 9x = 18 \]
Response area: \(9x = 18\)
Step 4: Use Division Property of Equality: Divide both sides by \( 9 \): \[ \frac{9x}{9} = \frac{18}{9} \]
This simplifies to: \[ x = 2 \]
Response area: \(x = 2\)