Question

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

Answer 1

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: \( x = 2 \)