Let's solve the inequality given in the image:

$-5(x - 7) + 5 > 0$

Step-by-step solution:

1. Distribute the $-5$ across the expression inside the parentheses: $-5(x - 7) = -5x + 35$ So, the inequality becomes: $-5x + 35 + 5 > 0$

2. Simplify the constant terms: $-5x + 40 > 0$

3. Isolate $x$ by first subtracting 40 from both sides: $-5x > -40$

4. Divide by $-5$ to solve for $x$, and reverse the inequality sign (since we're dividing by a negative number): $x < 8$

Solution:

The solution in interval notation is:

$(-\infty, 8)$

Would you like further details on any step? Feel free to ask!

Here are five related questions you might find helpful:

1. How do you solve inequalities involving parentheses?
2. What changes when dividing both sides of an inequality by a negative number?
3. Can you explain the difference between solving inequalities and equations?
4. How do you express inequality solutions in interval notation?
5. What are the general steps for solving linear inequalities?

Tip: Always remember to reverse the inequality sign when multiplying or dividing both sides of an inequality by a negative number!