Solve the equation for zz.
7 z plus z equals 7 z plus 97z+z=7z+9

The equation provided is:

\[
97z + z = 7z + 9
\]

### Step 1: Combine like terms on each side.

On the left-hand side, combine \( 97z \) and \( z \):

\[
97z + z = 98z
\]

The equation now becomes:

\[
98z = 7z + 9
\]

### Step 2: Move all terms involving \( z \) to one side.

Subtract \( 7z \) from both sides:

\[
98z - 7z = 9
\]

This simplifies to:

\[
91z = 9
\]

### Step 3: Solve for \( z \).

Divide both sides by 91:

\[
z = \frac{9}{91}
\]

Simplify the fraction:

\[
z = \frac{1}{10}
\]

### Final Answer:
\[
z = \frac{1}{10}
\]

Would you like more details or explanations on any step? Here are five related questions you can explore:

1. How do you combine like terms in algebra?
2. What are the properties of equality used in solving linear equations?
3. How do you simplify fractions?
4. What happens if the equation includes variables on both sides?
5. How do you handle more complex equations with multiple variables?

**Tip**: Always check your solution by substituting the value back into the original equation.

Solve the equation for z: 97z + z = 7z + 9

Learn how to solve the linear equation 97z + z = 7z + 9 with step-by-step guidance. This problem covers essential algebraic concepts, including combining like terms and applying the properties of equality. Suitable for students in Grades 6-8.

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