To solve the inequality \( 7 - 10x > -5 \):

### Step 1: Subtract 7 from both sides
\[
7 - 10x - 7 > -5 - 7
\]
\[
-10x > -12
\]

### Step 2: Divide both sides by \(-10\)
Since we are dividing by a negative number, we must **reverse the inequality sign**:
\[
x < \frac{-12}{-10}
\]
\[
x < 1.2
\]

### Final Answer:
\[
x < 1.2
\]

Would you like more details on this solution?

Here are 5 related questions:
1. How do we solve inequalities with fractions?
2. What happens when multiplying or dividing inequalities by negative numbers?
3. Can you graph the solution \(x < 1.2\)?
4. How do inequalities change if the problem involves absolute values?
5. What are compound inequalities?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing by a negative number!

Learn how to solve the inequality 7 - 10x > -5 with a detailed step-by-step solution. This algebra problem demonstrates key concepts, including inequality transformations and the rule for dividing by negative numbers. Suitable for students in Grades 6-8.

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