Solve the following system of inequations:
`-2-(x)/(4)le(1+x)/(3),3-xlt4(x-3)`.

Answer

To solve the system of inequations \(-2 - \frac{x}{4} \leq \frac{1+x}{3}\) and \(3 - x < 4(x - 3)\), we will break it down step by step.

### Step 1: Solve the first inequation \(-2 - \frac{x}{4} \leq \frac{1+x}{3}\)

1. Start with the given inequation:
\[ -2 - \frac{x}{4} \leq \frac{1+x}{3} \]

2. To eliminate the fractions, find a common denominator. The least common multiple (LCM) of 4 and 3 is 12. Multiply the entire inequation by 12:
\[ 12 \left(-2 - \frac{x}{4}\right) \leq 12 \left(\frac{1+x}{3}\right) \]
This simplifies to:
\[ -24 - 3x \leq 4 + 4x \]

3. Rearranging the terms gives:
\[ -24 - 4 \leq 4x + 3x \]
\[ -28 \leq 7x \]

4. Divide both sides by 7:
\[ -4 \leq x \]
or
\[ x \geq -4 \]

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

1. Start with the given inequation:
\[ 3 - x < 4(x - 3) \]

2. Distribute on the right side:
\[ 3 - x < 4x - 12 \]

3. Rearranging gives:
\[ 3 + 12 < 4x + x \]
\[ 15 < 5x \]

4. Divide both sides by 5:
\[ 3 < x \]
or
\[ x > 3 \]

### Step 3: Combine the results

From the first inequation, we have:
\[ x \geq -4 \]
From the second inequation, we have:
\[ x > 3 \]

### Conclusion

The solution to the system of inequations is:
\[ x > 3 \]