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 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 \( 2 \).