Question

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

Answer 1

To solve the equation \( 5x - 12 - 6x = -10x + 7 - 1 \), let's follow the steps to fill in the blanks:

1. **Combine like terms on both sides.**
\[
5x - 6x - 12 = -10x + 7 - 1
\]
Which simplifies to:
\[
-x - 12 = -10x + 6
\]

2. **Add \(10x\) to both sides to eliminate \(x\) from the right side.**
\[
-x + 10x - 12 = -10x + 10x + 6
\]
Simplifying gives:
\[
9x - 12 = 6
\]

3. **Add 12 to both sides to isolate the term with \(x\).**
\[
9x - 12 + 12 = 6 + 12
\]
This results in:
\[
9x = 18
\]

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

Putting it all together, the completed steps are:
1. \( -x - 12 = -10x + 6 \)
2. \( -x + 10x - 12 = 6 \)
3. \( 9x - 12 + 12 = 6 + 12 \)
4. \( x = \frac{18}{9} \)

Finally, we find that \( x = 2 \).