If `3x - 2 ( 4- 3x) lt 2x - 5 lt 3x + 3,` then the value of x is.

Options

A. 1
B. 2
C. 5
D. 0

Answer

To solve the inequality \( 3x - 2(4 - 3x) < 2x - 5 < 3x + 3 \), we will break it down into two parts:

1. Solve \( 3x - 2(4 - 3x) < 2x - 5 \)
2. Solve \( 2x - 5 < 3x + 3 \)

### Step 1: Solve \( 3x - 2(4 - 3x) < 2x - 5 \)

1. Distribute the \(-2\) in the left side:
\[ 3x - 8 + 6x < 2x - 5 \]
This simplifies to:
\[ 9x - 8 < 2x - 5 \]

2. Move \(2x\) to the left side:
\[ 9x - 2x - 8 < -5 \]
This simplifies to:
\[ 7x - 8 < -5 \]

3. Add \(8\) to both sides:
\[ 7x < 3 \]

4. Divide by \(7\):
\[ x < \frac{3}{7} \]

### Step 2: Solve \( 2x - 5 < 3x + 3 \)

1. Move \(3x\) to the left side:
\[ 2x - 3x - 5 < 3 \]
This simplifies to:
\[ -x - 5 < 3 \]

2. Add \(5\) to both sides:
\[ -x < 8 \]

3. Multiply by \(-1\) (remember to flip the inequality):
\[ x > -8 \]

### Step 3: Combine the results

From the two inequalities we have:
1. \( x < \frac{3}{7} \)
2. \( x > -8 \)

Thus, the solution is:
\[ -8 < x < \frac{3}{7} \]

### Conclusion

The values of \(x\) that satisfy the original inequality are those that lie between \(-8\) and \(\frac{3}{7}\).