Certainly! Let's walk through the steps to solve the equation [tex]\(\frac{-22 + 3x}{3x + 7} = 2\)[/tex].
To begin isolating the variable [tex]\(x\)[/tex], you should:
### Step 1:
Multiply both sides by [tex]\(3x + 7\)[/tex].
This eliminates the fraction, allowing us to deal directly with a simpler equation.
After multiplying both sides by [tex]\(3x + 7\)[/tex], the equation becomes:
### Step 2:
[tex]\[
-22 + 3x = 2 \cdot (3x + 7)
\][/tex]
Expand the right-hand side:
[tex]\[
-22 + 3x = 6x + 14
\][/tex]
### Step 3:
Isolate [tex]\(x\)[/tex]. To do this, move all terms involving [tex]\(x\)[/tex] to one side and constant terms to the other side:
[tex]\[
3x - 6x = 14 + 22
\][/tex]
### Step 4:
Combine like terms:
[tex]\[
-3x = 36
\][/tex]
### Step 5:
Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{36}{-3} = -12
\][/tex]
So, the solution of the equation is [tex]\(x = -12\)[/tex].
Given options for the steps:
1. How do you begin isolating the variable [tex]\(x\)[/tex] to one side of the equation?
2. The solution of the equation is?
Here are the correct selections:
1. Multiply both sides by [tex]\(3x + 7\)[/tex].
2. [tex]\(x = -12\)[/tex].
Thus:
```
Step 1: Multiply both sides by 3 x + 7.
The solution of the equation is x = -12.
```
