Question

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

Answer 1

the options are ： -12-12=－102+6
:: 5 - 18x = -3x - 1
:: 1x - 12 = -10x + 6
:: -12 = -11x + 6
:: 9x - 12 = 6
:: -12 = -9x + 6
:: -18 = 9x
:: -6 = -9х
-18 = -9x
:: x= 0
•: X = 1
Z =x
': X =-2

Answer 2

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

1. **Combine like terms on both sides of the equation**:

On the left side:
\[
5x - 6x - 12 = -x - 12
\]

On the right side:
\[
-10x + 7 - 1 = -10x + 6
\]

So the equation now is:
\[
-x - 12 = -10x + 6
\]

2. **Add \(10x\) to both sides to get all \(x\) terms on one side**:
\[
-x + 10x - 12 = 6
\]

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

3. **Add 12 to both sides**:
\[
9x - 12 + 12 = 6 + 12
\]

So we have:
\[
9x = 18
\]

4. **Divide by 9 to solve for \(x\)**:
\[
x = \frac{18}{9} = 2
\]

The final solution is:
\[
x = 2
\]

Thus, the steps in solving the equation were:
1. Combine like terms.
2. Add \(10x\) to both sides.
3. Add 12 to both sides.
4. Divide by 9 to solve for \(x\).

Answer 3

Based on the equation you provided earlier and the options available, let's fill in the blanks step by step. The original equation is:

\[ 5x - 12 - 6x = -10x + 7 - 1 \]

On simplifying, we derived:

1. Combine like terms:
- On the left side: \(5x - 6x - 12 = -x - 12\)
- On the right side: \(-10x + 7 - 1 = -10x + 6\)

So we have:
\[ -x - 12 = -10x + 6 \]

Now, let's follow through the correct option sequence based on simplifications.

1. **Combine like terms**:
- \(-12 - 12 = -10x + 6\)

This doesn't match any options. Let's reframe this step using the options provided.

2. Use the option assigning to combine terms:
- Using the option: **1x - 12 = -10x + 6**

Which is the combined left and right from our earlier calculation.

3. **Now, isolate x**:
- We can rearrange to:
\[ 1x + 10x = 6 + 12 \]
- Which gives:
\[ 11x = 18 \]
- This combined scenario should have a representation of **9x - 12 = 6** to gain continuity.

4. **Continuing from \(9x - 12 = 6\)**, add \(12\):
- \(9x = 18\)

5. **Divide by 9**:
- \(x = 2\)

None of the provided options directly match the calculations (as they typically start with simplifying or reorganizing parts).

### Additional possible options from what was derived:
- \(9x - 12 = 6\)
- \(x = 2\)

If you're looking to fill the blanks directly, the likely option choices would align to extract through:

1. Combine \(1x - 12 = -10x + 6\)
2. Apply remains, \(-12 = -10x + 6\)
3. Gathering, subsequently realizing views across \(-12 + 12 = −10x + 6 + 12\) helps showcase if iterative expressions are consistent.

The end solution remains \(x = 2\) unless clarified for targeting specific segments within presented options.