To solve the inequality $5(5x - 5) - 6x > -2$, follow these steps:

Step-by-Step Solution:

1. Distribute the $5$ into the expression $5x - 5$: $5(5x - 5) = 25x - 25$ So the inequality becomes: $25x - 25 - 6x > -2$

2. Combine like terms:
   Group the $x$-terms and constants: $(25x - 6x) - 25 > -2$ $19x - 25 > -2$

3. Isolate the $x$-term:
   Add $25$ to both sides to move the constant to the right: $19x > -2 + 25$ $19x > 23$

4. Solve for $x$:
   Divide both sides by $19$: $x > \frac{23}{19}$

Final Answer:

The solution to the inequality is: $x > \frac{23}{19}$

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Related Questions:

1. How do you solve inequalities with variables on both sides?
2. What is the difference between solving an equation and an inequality?
3. How would the solution change if it were $\geq$ instead of $>$?
4. How can you graph the solution $x > \frac{23}{19}$ on a number line?
5. What happens if we multiply or divide by a negative number in an inequality?

Tip: When multiplying or dividing an inequality by a negative number, always reverse the inequality sign!