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.