Question

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

step one combine like terms

Answer 1

To solve the equation \( 5x - 12 - 6x = -10x + 7 - 1 \), we can follow these steps:

**Step 1: Combine like terms on both sides.**

On the left side:
- Combine \( 5x \) and \( -6x \):
\[
5x - 6x = -1x \quad \text{(or just } -x\text{)}
\]
- So the left side becomes:
\[
-x - 12
\]

On the right side:
- Simplify \( 7 - 1 \):
\[
7 - 1 = 6
\]
- So the right side becomes:
\[
-10x + 6
\]

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

**Step 2: Add \( 10x \) to both sides to isolate terms containing \( x \).**

\[
-x + 10x - 12 = 6
\]
This simplifies to:
\[
9x - 12 = 6
\]

**Step 3: Add 12 to both sides to isolate the \( x \) term.**

\[
9x - 12 + 12 = 6 + 12
\]
This simplifies to:
\[
9x = 18
\]

**Step 4: Divide both sides by 9 to solve for \( x \).**

\[
x = \frac{18}{9}
\]
This simplifies to:
\[
x = 2
\]

Thus, the final solution is:
\[
x = 2
\]