Let's solve the inequality:

Given: $5x - 7(x + 1) > -9$

Step 1: Distribute $-7$ to the terms inside the parentheses:

$5x - 7x - 7 > -9$

Step 2: Combine like terms:

$(5x - 7x) - 7 > -9$ $-2x - 7 > -9$

Step 3: Add $7$ to both sides:

$-2x > -9 + 7$ $-2x > -2$

Step 4: Divide both sides by $-2$ (remember to flip the inequality when dividing by a negative number):

$x < \frac{-2}{-2}$ $x < 1$

Final solution:

$x < 1$

Would you like a detailed explanation of any step, or do you have any questions?

Here are 5 related questions to help you practice:

1. Solve: $3x - 4(x + 2) > 8$
2. Solve: $7 - 2(x + 3) \geq 3x - 5$
3. Solve: $5(2x - 1) - 3x \leq 9$
4. Solve and graph the inequality: $x + 5 > 2x - 4$
5. Solve the compound inequality: $3x + 2 > 8$ and $5x - 7 \leq 3$

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