Fill in the blanks to follow the steps in solving the equation: 5x - 12 - 6x = - 10x + 7 - 1

Question

Step 1: Combine like terms to get: Response area

Step 2: Get the x-terms on the same side of the equation: Response area

Step 3: Get the constants on the same side of the equation: Response area

Step 4: Use Division Property of Equality: Response area

options for the response areas:
-x - 12 = -10x + 6
5x - 18 = -3x - 1
x - 12 = -10x - 6
9x - 12 = 6
-12 = -11x + 6
8x - 18 = -1
8x = 19
9x = 18
-18 = -11x
x = 2
x = 0
x = 11/18

Answer 1

Let's go through the steps one by one to solve the equation \( 5x - 12 - 6x = -10x + 7 - 1 \):

Step 1: Combine like terms

On the left-hand side, combine \( 5x - 6x \): \[ -x - 12 = -10x + 7 - 1 \] On the right-hand side, combine \( 7 - 1 \): \[ -x - 12 = -10x + 6 \] Response Area for Step 1: \[ -x - 12 = -10x + 6 \]

Step 2: Get the x-terms on the same side of the equation

Add \( 10x \) to both sides: \[ -x + 10x - 12 = 6 \] This simplifies to: \[ 9x - 12 = 6 \] Response Area for Step 2: \[ 9x - 12 = 6 \]

Step 3: Get the constants on the same side of the equation

Add \( 12 \) to both sides: \[ 9x - 12 + 12 = 6 + 12 \] This simplifies to: \[ 9x = 18 \] Response Area for Step 3: \[ 9x = 18 \]

Step 4: Use Division Property of Equality

Divide both sides by \( 9 \): \[ x = 2 \] Response Area for Step 4: \[ x = 2 \]

Putting it all together:

1. Step 1: -x - 12 = -10x + 6
2. Step 2: 9x - 12 = 6
3. Step 3: 9x = 18
4. Step 4: x = 2