What is the larger integer value of p that satisfies the equality `4+3pltp+1`?

Options

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

Answer

To solve the inequality \( 4 + 3p < p + 1 \), we will follow these steps:

### Step 1: Rearrange the inequality
Start with the original inequality:
\[ 4 + 3p < p + 1 \]

### Step 2: Subtract \( p \) from both sides
To isolate \( p \), we subtract \( p \) from both sides:
\[ 4 + 3p - p < p - p + 1 \]
This simplifies to:
\[ 4 + 2p < 1 \]

### Step 3: Subtract 4 from both sides
Next, we subtract 4 from both sides to further isolate \( p \):
\[ 4 - 4 + 2p < 1 - 4 \]
This simplifies to:
\[ 2p < -3 \]

### Step 4: Divide by 2
Now, we divide both sides by 2 to solve for \( p \):
\[ p < -\frac{3}{2} \]
This is equivalent to:
\[ p < -1.5 \]

### Step 5: Identify the largest integer value
The largest integer value of \( p \) that satisfies \( p < -1.5 \) is:
\[ p = -2 \]

Thus, the final answer is:
\[ \text{The largest integer value of } p \text{ is } -2. \]

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