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!