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I see the image contains two inequalities. Let me solve each of them step by step:

### 17. Solve the inequality:

\[
-4x + 2(x - 3) \geq 4x - (3 + 5x) - 7
\]

#### Step-by-step solution:

1. Distribute the 2 on the left side:
   \[
   -4x + 2(x - 3) = -4x + 2x - 6 = -2x - 6
   \]
   So, the inequality becomes:
   \[
   -2x - 6 \geq 4x - (3 + 5x) - 7
   \]

2. Simplify the right side:
   \[
   4x - (3 + 5x) - 7 = 4x - 3 - 5x - 7 = -x - 10
   \]
   Now the inequality is:
   \[
   -2x - 6 \geq -x - 10
   \]

3. Add \(x\) to both sides:
   \[
   -2x + x - 6 \geq -10
   \]
   \[
   -x - 6 \geq -10
   \]

4. Add 6 to both sides:
   \[
   -x \geq -4
   \]

5. Multiply both sides by \(-1\) (and reverse the inequality):
   \[
   x \leq 4
   \]

The solution to the inequality is:
\[
x \leq 4
\]

---

### 18. Solve the compound inequality:

\[
-10 < 3x - 4 \leq 14
\]

#### Step-by-step solution:

1. Split the inequality into two parts and solve each:

   - Solve the left part:
     \[
     -10 < 3x - 4
     \]
     Add 4 to both sides:
     \[
     -6 < 3x
     \]
     Divide by 3:
     \[
     -2 < x
     \]
     This is:
     \[
     x > -2
     \]

   - Solve the right part:
     \[
     3x - 4 \leq 14
     \]
     Add 4 to both sides:
     \[
     3x \leq 18
     \]
     Divide by 3:
     \[
     x \leq 6
     \]

2. Combine both results:
   \[
   -2 < x \leq 6
   \]

The solution to the compound inequality is:
\[
-2 < x \leq 6
\]

---

Would you like a detailed explanation of any part, or perhaps the graph for these solutions?

Here are 5 related questions for further practice:
1. How do you graph the solution of the inequality \(x \leq 4\)?
2. What happens if the inequality involves multiplying or dividing by a negative number?
3. Can you solve the inequality \(3x + 5 > 2x - 7\)?
4. How do you solve absolute value inequalities?
5. Can you solve a system of inequalities, such as \(x + y \geq 3\) and \(2x - y < 5\)?

**Tip:** When solving inequalities, always reverse the inequality sign when multiplying or dividing both sides by a negative number.

-4x + 2(x - 3) ≥ 4x - (3 + 5x) - 7 and -10 < 3x - 4 ≤ 14

Learn how to solve the linear inequalities -4x + 2(x - 3) ≥ 4x - (3 + 5x) - 7 and -10 < 3x - 4 ≤ 14 with detailed step-by-step explanations. This problem covers key algebraic concepts and is suitable for students in Grades 9-11.

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