We are given two inequalities:

1. \( -33 > -4x - 5 \)
2. \( -4x - 5 \geq -49 \)

We need to solve both inequalities individually.

### First inequality: \( -33 > -4x - 5 \)

1. Add 5 to both sides:
   \[
   -33 + 5 > -4x
   \]
   \[
   -28 > -4x
   \]

2. Divide both sides by \(-4\). Remember, when dividing by a negative number, the inequality sign reverses:
   \[
   \frac{-28}{-4} < x
   \]
   \[
   7 < x
   \]
   or
   \[
   x > 7
   \]

### Second inequality: \( -4x - 5 \geq -49 \)

1. Add 5 to both sides:
   \[
   -4x \geq -49 + 5
   \]
   \[
   -4x \geq -44
   \]

2. Divide both sides by \(-4\), reversing the inequality:
   \[
   \frac{-4x}{-4} \leq \frac{-44}{-4}
   \]
   \[
   x \leq 11
   \]

### Combined solution:
The solution to the compound inequality is:
\[
7 < x \leq 11
\]
or
\[
x \in (7, 11]
\]

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. Solve: \( 2x - 5 > 3 \) and \( 3x + 2 \leq 17 \).
2. Solve the inequality: \( -5x + 7 \geq -3x - 5 \).
3. What is the solution set for \( -2x + 4 < 6 \) or \( 3x - 5 \geq 7 \)?
4. Solve and graph: \( 5x - 10 < 0 \) and \( 2x + 8 \geq 12 \).
5. Solve for \( x \): \( 4x - 3 > 2x + 7 \).

**Tip**: Always reverse the inequality sign when multiplying or dividing both sides by a negative number.

−33 > −4x − 5 or −4x − 5 ≥ −49

Learn how to solve compound inequalities involving linear equations, such as −33 > −4x − 5 and −4x − 5 ≥ −49. This detailed step-by-step solution teaches key algebraic concepts like reversing inequalities when dividing by a negative number. Suitable for students in Grades 8-10.

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