If `3x + 4 (1 -x) gt 5x - 2 gt 4x -4,` then the value of x is

Options

A. 2
B. `-2`
C. 0
D. `-3`

Answer

To solve the inequality \(3x + 4(1 - x) > 5x - 2 > 4x - 4\), we can break it down into two parts and solve each part step by step.

### Step 1: Solve the first inequality \(3x + 4(1 - x) > 5x - 2\)

1. Distribute the 4 in the left side:
\[ 3x + 4 - 4x > 5x - 2 \]

2. Combine like terms on the left side:
\[ -x + 4 > 5x - 2 \]

3. Add \(x\) to both sides:
\[ 4 > 6x - 2 \]

4. Add 2 to both sides:
\[ 6 > 6x \]

5. Divide both sides by 6:
\[ 1 > x \quad \text{or} \quad x < 1 \]

### Step 2: Solve the second inequality \(5x - 2 > 4x - 4\)

1. Subtract \(4x\) from both sides:
\[ 5x - 4x - 2 > -4 \]

2. Simplify:
\[ x - 2 > -4 \]

3. Add 2 to both sides:
\[ x > -2 \]

### Step 3: Combine the results

From the two inequalities, we have:
1. \(x < 1\)
2. \(x > -2\)

Thus, the solution to the compound inequality is:
\[ -2 < x < 1 \]

### Conclusion

The value of \(x\) lies between \(-2\) and \(1\). Any value within this range satisfies the original inequality.