If `4 (2x -4) - 2 gt 3x -1 = 4x -7 , ` then x can take which of the following values ?

Options

A. 7
B. 6
C. 2
D. 0

Answer

To solve the inequality \(4(2x - 4) - 2 > 3x - 1 = 4x - 7\), we will break it down step by step.

### Step 1: Distribute the terms
Start by distributing the \(4\) in the expression \(4(2x - 4)\):

\[ 4(2x) - 4(4) - 2 > 3x - 1 \]

This simplifies to:

\[ 8x - 16 - 2 > 3x - 1 \]

### Step 2: Combine like terms
Now, combine the constants on the left side:

\[ 8x - 18 > 3x - 1 \]

### Step 3: Move all terms involving \(x\) to one side
Subtract \(3x\) from both sides:

\[ 8x - 3x - 18 > -1 \]

This simplifies to:

\[ 5x - 18 > -1 \]

### Step 4: Isolate \(x\)
Now, add \(18\) to both sides:

\[ 5x > 17 \]

### Step 5: Solve for \(x\)
Finally, divide both sides by \(5\):

\[ x > \frac{17}{5} \]

### Step 6: Convert to decimal (if necessary)
The fraction \(\frac{17}{5}\) can be converted to a decimal:

\[ x > 3.4 \]

### Conclusion
The solution indicates that \(x\) can take any value greater than \(3.4\). Among the options provided (7, 6, 2, 0), the only value that satisfies this condition is \(6\).