Name three values that satisfy the inequality 
5(3z−7)>12

Let's solve the inequality \( 5(3z - 7) > 12 \) step by step to find values of \( z \) that satisfy it.

### Step 1: Distribute the 5
\[
5(3z - 7) > 12
\]
\[
15z - 35 > 12
\]

### Step 2: Add 35 to both sides
\[
15z > 12 + 35
\]
\[
15z > 47
\]

### Step 3: Divide both sides by 15
\[
z > \frac{47}{15}
\]
\[
z > 3.13\ (\text{approximately})
\]

### Conclusion:
Any value of \( z \) greater than 3.13 will satisfy the inequality. Three possible values for \( z \) could be:
- \( z = 4 \)
- \( z = 5 \)
- \( z = 6 \)

These values satisfy the inequality \( 5(3z - 7) > 12 \).

Would you like further details or have any questions?

Here are 5 questions to expand on this topic:
1. How do you check if a given value satisfies an inequality?
2. Can you explain how to graph the solution to this inequality on a number line?
3. What happens to the inequality when you divide by a negative number?
4. How do you solve a system of inequalities involving two variables?
5. How do inequalities change when you involve absolute values?

**Tip:** When solving inequalities, always be cautious when multiplying or dividing by negative numbers—they reverse the inequality sign!

Name three values that satisfy the inequality 5(3z−7)>12

Learn how to solve the inequality 5(3z - 7) > 12 with a step-by-step solution. This problem involves applying the distributive property, solving linear inequalities, and understanding how to manipulate inequalities. Suitable for students in Grades 7-9.

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