If `2x -1 lt 5x + 2 and 2x + 5 lt 6 - 3x,` then x can take which of the following values ?

Options

A. 1
B. 0
C. 2
D. `-2`

Answer

To solve the inequalities given in the question, we will break it down step by step.

### Step 1: Solve the first inequality
The first inequality is:
\[ 2x - 1 < 5x + 2 \]

To solve for \( x \), we will first isolate \( x \) on one side.

1. Subtract \( 2x \) from both sides:
\[ -1 < 5x - 2x + 2 \]
\[ -1 < 3x + 2 \]

2. Next, subtract 2 from both sides:
\[ -1 - 2 < 3x \]
\[ -3 < 3x \]

3. Now, divide both sides by 3:
\[ -1 < x \]
or
\[ x > -1 \]

### Step 2: Solve the second inequality
The second inequality is:
\[ 2x + 5 < 6 - 3x \]

Again, we will isolate \( x \):

1. Add \( 3x \) to both sides:
\[ 2x + 3x + 5 < 6 \]
\[ 5x + 5 < 6 \]

2. Subtract 5 from both sides:
\[ 5x < 6 - 5 \]
\[ 5x < 1 \]

3. Divide both sides by 5:
\[ x < \frac{1}{5} \]

### Step 3: Combine the results
From the two inequalities we have:
1. \( x > -1 \)
2. \( x < \frac{1}{5} \)

This means that \( x \) must satisfy:
\[ -1 < x < \frac{1}{5} \]

### Step 4: Determine possible values for \( x \)
The values that \( x \) can take are any real numbers that lie between -1 and \( \frac{1}{5} \).

### Conclusion
Since the question asks which of the following values \( x \) can take, we need to check the provided options. If one of the options is 0, then \( x \) can take that value because:
\[ -1 < 0 < \frac{1}{5} \]