To solve for \( z \) in the equation:

\[
-5z + 7z = 44 - 26
\]

### Step 1: Simplify both sides of the equation.
- Combine like terms on the left side:

\[
2z = 44 - 26
\]

- Simplify the right side:

\[
2z = 18
\]

### Step 2: Solve for \( z \).
- Divide both sides by 2:

\[
z = \frac{18}{2}
\]

\[
z = 9
\]

So, the solution is \( z = 9 \).

Would you like more details, or do you have any questions?

Here are five related questions to explore further:
1. What happens if we change the coefficients in the equation?
2. How do we solve a similar equation with a quadratic term?
3. What is the solution if the equation were \( -5z + 7z + 4 = 44 - 26 \)?
4. How do you graph the equation \( -5z + 7z = 44 - 26 \)?
5. How do you solve the equation if there's a fraction involved?

**Tip:** When simplifying equations, always combine like terms first before isolating the variable.

Step-by-step guide to solve the linear equation -5z + 7z = 44 - 26. This problem demonstrates algebraic concepts such as combining like terms and simplifying equations, suitable for students in Grades 6-8.

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