https://file.aiquickdraw.com/mathbot/file/1727462817778055qeovo.jpg

The inequality given in the image is:

\[
8 + 7 - 2z > -6z + z + 6
\]

Let's solve this step-by-step:

1. **Simplify both sides**:

   - Left-hand side: \( 8 + 7 - 2z = 15 - 2z \).
   - Right-hand side: \( -6z + z + 6 = -5z + 6 \).

Thus, the inequality becomes:

\[
15 - 2z > -5z + 6
\]

2. **Isolate the variable \( z \)** by adding \( 5z \) to both sides:

\[
15 - 2z + 5z > -5z + 6 + 5z
\]
\[
15 + 3z > 6
\]

3. **Subtract 15 from both sides**:

\[
15 + 3z - 15 > 6 - 15
\]
\[
3z > -9
\]

4. **Divide by 3**:

\[
z > -3
\]

So, the solution to the inequality is:

\[
z > -3
\]

Would you like more details or have any questions?

### Related Questions
1. How would the inequality change if we reversed the inequality sign?
2. What happens if we have \( z \) terms on both sides with positive coefficients?
3. Can this inequality be represented graphically on a number line?
4. What does it mean for a value to satisfy an inequality?
5. How would the solution change if we had a quadratic term, like \( z^2 \)?

**Tip**: When solving inequalities, remember that multiplying or dividing both sides by a negative number reverses the inequality sign.

Solve the inequality 8 + 7 - 2z > -6z + z + 6

Learn how to solve the linear inequality 8 + 7 - 2z > -6z + z + 6 with a detailed step-by-step solution. This problem covers key algebraic concepts, including simplifying linear expressions and solving inequalities. Suitable for students in Grades 7-9.

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