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Consider the equation
-22 + 3x/3z+7
=2

How do you begin isolating the variable x to one side of the equation?
The solution of the equation is

To isolate the variable \( x \) in the given equation:

\[
-22 + \frac{3x}{3z} + 7 = 2
\]

### Step 1: Combine constants on the left-hand side
First, simplify the constants on the left side of the equation:
\[
-22 + 7 = -15
\]
So, the equation becomes:
\[
-15 + \frac{3x}{3z} = 2
\]

### Step 2: Move the constant to the other side
Next, move the constant \( -15 \) to the other side of the equation by adding 15 to both sides:
\[
\frac{3x}{3z} = 2 + 15
\]
\[
\frac{3x}{3z} = 17
\]

### Step 3: Simplify the coefficient
The fraction \( \frac{3x}{3z} \) simplifies to \( \frac{x}{z} \), so the equation becomes:
\[
\frac{x}{z} = 17
\]

### Step 4: Solve for \( x \)
Finally, multiply both sides of the equation by \( z \) to isolate \( x \):
\[
x = 17z
\]

### The solution of the equation is:
\[
x = 17z
\]

Would you like more details or have any other questions?

Here are 5 related questions you can try:
1. What happens if \( z = 0 \) in the solution \( x = 17z \)?
2. How would the process change if the equation were \( -22 + \frac{3x}{5z} + 7 = 2 \)?
3. Can you solve the equation \( -15 + \frac{3x}{3z} = 10 \)?
4. How do you check if your solution to this equation is correct?
5. What other methods could you use to solve for \( x \)?

**Tip:** Always simplify constants and fractions early on to make the equation easier to manage!

Consider the equation -22 + 3x/3z + 7 = 2. How do you begin isolating the variable x to one side of the equation?

Learn how to isolate the variable x in the algebraic equation -22 + 3x/3z + 7 = 2. This step-by-step solution demonstrates basic algebraic manipulation and fraction simplification, suitable for students in Grades 8-10.

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