Solve the following system of inequations:
`4x-5lt11,-3x-4ge8`.

Answer

To solve the system of inequations \(4x - 5 < 11\) and \(-3x - 4 \geq 8\), we will solve each inequation step by step.

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

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 gives us:
\[ x < 4 \]

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

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 when dividing by a negative number)
\[ \frac{-3x}{-3} \leq \frac{12}{-3} \]
This gives us:
\[ x \leq -4 \]

### Step 3: Combine the results

From the first inequation, we have:
\[ x < 4 \]
From the second inequation, we have:
\[ x \leq -4 \]

### Step 4: Determine the solution set

The solution set is the intersection of the two results:
- \(x < 4\) means all numbers less than 4.
- \(x \leq -4\) means all numbers less than or equal to -4.

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

### Final Answer:
The solution to the system of inequations is:
\[ x \in (-\infty, -4] \]

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