Find the solution set of `4x-5lt11,-3x-4ge8`.

Answer

To solve the inequalities \(4x - 5 < 11\) and \(-3x - 4 \geq 8\), we will break down each inequality step by step.

### Step 1: Solve the first inequality \(4x - 5 < 11\)

1. **Add 5 to both sides**:
\[ 4x - 5 + 5 < 11 + 5 \]
This simplifies to:
\[ 4x < 16 \]

2. **Divide both sides by 4**:
\[ \frac{4x}{4} < \frac{16}{4} \]
This simplifies to:
\[ x < 4 \]

### Step 2: Solve the second inequality \(-3x - 4 \geq 8\)

1. **Add 4 to both sides**:
\[ -3x - 4 + 4 \geq 8 + 4 \]
This simplifies to:
\[ -3x \geq 12 \]

2. **Divide both sides by -3** (remember to reverse the inequality sign):
\[ \frac{-3x}{-3} \leq \frac{12}{-3} \]
This simplifies to:
\[ x \leq -4 \]

### Step 3: Combine the results

Now we have two inequalities:
1. \(x < 4\)
2. \(x \leq -4\)

### Step 4: Determine the solution set

The solution set is the intersection of the two inequalities. The first inequality allows values of \(x\) up to but not including 4, while the second inequality allows values of \(x\) down to -4, inclusive.

Thus, the solution set is:
\[ x \in (-\infty, -4] \]

### Final Answer
The solution set of the given inequalities is:
\[ \{ x \mid x \in (-\infty, -4] \} \]

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