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!

Learn how to solve the linear inequality 5x - 7(x+1) > -9 step by step. This problem involves algebraic concepts like the distributive property, combining like terms, and reversing the inequality sign when dividing by a negative. Ideal for students in Grades 8-10.

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