To solve the equation \( 7 = -\frac{5}{6}z - 23 \) for \( z \), follow these steps:

### Step 1: Add 23 to both sides of the equation.
\[
7 + 23 = -\frac{5}{6}z
\]
\[
30 = -\frac{5}{6}z
\]

### Step 2: Multiply both sides of the equation by the reciprocal of \(-\frac{5}{6}\), which is \(-\frac{6}{5}\).
\[
z = 30 \times \left(-\frac{6}{5}\right)
\]
\[
z = -36
\]

So, the solution is \( z = -36 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the solution change if the equation was \( 7 = -\frac{5}{6}z + 23 \)?
2. What is the general method for solving linear equations with fractions?
3. How do you check if your solution to an equation is correct?
4. What happens if the fraction's denominator includes a variable?
5. Can you solve for \( z \) in the equation \( 7z = -5/6z - 23 \)?

**Tip:** Always try to isolate the variable on one side of the equation by performing inverse operations step by step.

Learn how to solve the linear equation 7 = -5/6z - 23 step-by-step with a detailed solution. This problem covers key algebraic concepts, including linear equations, fractions, and inverse operations. Suitable for students in Grades 7-9.

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