Question

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

5x−12−6x=−10x+7−1
Step 1: Combine like terms _______________

Step 2: Get x-terms on same side of equation _______________

Step 3: Get constants on same side of equation _______________

Step 4: Get the x by itself by using the inverse operation _______________

Answer 1

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

**Step 1: Combine like terms**
Combine \(5x\) and \(-6x\) on the left side, and \(7\) and \(-1\) on the right side.
\[
(5x - 6x) - 12 = -10x + (7 - 1)
\]
This simplifies to:
\[
-x - 12 = -10x + 6
\]

**Step 2: Get x-terms on same side of equation**
Add \(10x\) to both sides to get all the \(x\) terms on one side:
\[
-x + 10x - 12 = 6
\]
This simplifies to:
\[
9x - 12 = 6
\]

**Step 3: Get constants on same side of equation**
Add \(12\) to both sides to move the constant terms:
\[
9x - 12 + 12 = 6 + 12
\]
This simplifies to:
\[
9x = 18
\]

**Step 4: Get the x by itself by using the inverse operation**
Divide both sides by \(9\):
\[
x = \frac{18}{9}
\]
This simplifies to:
\[
x = 2
\]

Putting it all together:

- **Step 1:** Combine like terms: \(5x - 6x = -x\) and \(7 - 1 = 6\)
- **Step 2:** Get x-terms on same side of equation: Add \(10x\) to both sides
- **Step 3:** Get constants on same side of equation: Add \(12\) to both sides
- **Step 4:** Get the x by itself by using the inverse operation: Divide by \(9\)

So the completed steps are:

1. Combine like terms: \(5x - 6x = -x\) and \(7 - 1 = 6\)
2. Get x-terms on the same side of the equation: Add \(10x\) to both sides
3. Get constants on the same side of the equation: Add \(12\) to both sides
4. Get the x by itself by using the inverse operation: Divide by \(9\)