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

Question

5x−12−6x=−10x+7−1

step one : combine like terms

Answer 1

To fill in the blanks following the steps to solve the equation \( 5x - 12 - 6x = -10x + 7 - 1 \), let's proceed step by step.

Step One: Combine Like Terms

On the left side:

• \( 5x - 6x = -x \)
• Thus, the left side simplifies to \(-x - 12\).

On the right side:

• Combine \( 7 - 1 \) which equals \( 6 \).
• Thus, the right side simplifies to \(-10x + 6\).

So, after combining like terms, we get: \[ -x - 12 = -10x + 6 \]

Step Two: Isolate the variable

Next, we will add \( 10x \) to both sides to get all terms involving \( x \) on one side: \[ -x + 10x - 12 = 6 \] This simplifies to: \[ 9x - 12 = 6 \]

Step Three: Solve for \( x \)

Now add \( 12 \) to both sides: \[ 9x - 12 + 12 = 6 + 12 \] This simplifies to: \[ 9x = 18 \]

Step Four: Divide to find \( x \)

Finally, divide both sides by \( 9 \): \[ x = \frac{18}{9} \] Which simplifies to: \[ x = 2 \]

Summary of Steps:

1. Combine like terms:
   • From \( 5x - 12 - 6x = -10x + 7 - 1 \) to \( -x - 12 = -10x + 6 \)
2. Isolate the variable:
   • From \( -x - 12 = -10x + 6 \) to \( 9x - 12 = 6 \)
3. Solve for \( x \):
   • From \( 9x - 12 = 6 \) to \( 9x = 18 \)
4. Divide to find \( x \):
   • From \( 9x = 18 \) to \( x = 2 \)

The value of \( x \) is \( 2 \).