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

Options

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

Answer

To solve the inequality \( 4(4x + 5) > 2x - 1 > 4x - 3 \), we will break it down into two separate inequalities and solve them step by step.

### Step 1: Solve the first part of the inequality
We start with the left part of the inequality:
\[ 4(4x + 5) > 2x - 1 \]

**Distributing the 4:**
\[ 16x + 20 > 2x - 1 \]

**Rearranging the inequality:**
Subtract \( 2x \) from both sides:
\[ 16x - 2x + 20 > -1 \]
\[ 14x + 20 > -1 \]

**Subtracting 20 from both sides:**
\[ 14x > -1 - 20 \]
\[ 14x > -21 \]

**Dividing both sides by 14:**
\[ x > -\frac{21}{14} \]
\[ x > -\frac{3}{2} \]

### Step 2: Solve the second part of the inequality
Now, we solve the right part of the inequality:
\[ 2x - 1 > 4x - 3 \]

**Rearranging the inequality:**
Subtract \( 2x \) from both sides:
\[ -1 > 4x - 2x - 3 \]
\[ -1 > 2x - 3 \]

**Adding 3 to both sides:**
\[ -1 + 3 > 2x \]
\[ 2 > 2x \]

**Dividing both sides by 2:**
\[ 1 > x \]
or
\[ x < 1 \]

### Step 3: Combine the results
From the two parts of the inequality, we have:
1. \( x > -\frac{3}{2} \)
2. \( x < 1 \)

Thus, combining these results, we get:
\[ -\frac{3}{2} < x < 1 \]

### Conclusion
The value of \( x \) lies between \(-\frac{3}{2}\) and \(1\).