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Fill in the blanks to follow the steps in solving the equation: 5x−12−6x=−10x+7−1 (4 points)

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5x−12−6x=−10x+7−1
Step 1: Combine like terms

1 answer

To solve the equation \( 5x−12−6x=−10x+7−1 \), we start by combining like terms.

Step 1: Combine like terms

On the left side:

  • Combine \( 5x \) and \( -6x \): \[ 5x - 6x = -1x \text{ (or } -x\text{)} \]

On the right side:

  • Simplify \( 7 - 1 \): \[ 7 - 1 = 6 \]

Now the equation looks like this: \[ -x - 12 = -10x + 6 \]

Step 2: Add \( 10x \) to both sides (to eliminate \( -10x \) on the right): \[ -x + 10x - 12 = 6 \] This simplifies to: \[ 9x - 12 = 6 \]

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

Step 4: Divide both sides by \( 9 \): \[ x = \frac{18}{9} \] This simplifies to: \[ x = 2 \]

So, the full progression is to organize as follows:

  1. Combine like terms:

    • Left side becomes \( -x - 12 \)
    • Right side becomes \( -10x + 6 \)

  2. Add \( 10x \)

  3. Add \( 12 \)

  4. Divide by \( 9 \)

Final answer: \( x = 2 \)