Simplify the equation and find value of p
`(p-2)//3={(p-1)//4}+1`

Options

A. P=17
B. P=12
C. P=14
D. P=18

Answer

To solve the equation \( \frac{p-2}{3} = \frac{p-1}{4} + 1 \), we will follow these steps:

### Step 1: Eliminate the fractions
To eliminate the fractions, we can multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 12.

\[ 12 \cdot \left(\frac{p-2}{3}\right) = 12 \cdot \left(\frac{p-1}{4} + 1\right) \]

### Step 2: Simplify both sides
Now, we simplify both sides:

\[ 4(p-2) = 3(p-1) + 12 \]

### Step 3: Distribute on both sides
Distributing on both sides gives us:

\[ 4p - 8 = 3p - 3 + 12 \]

### Step 4: Combine like terms on the right side
Now, combine like terms on the right side:

\[ 4p - 8 = 3p + 9 \]

### Step 5: Isolate \( p \)
Next, we will isolate \( p \) by subtracting \( 3p \) from both sides:

\[ 4p - 3p - 8 = 9 \]

This simplifies to:

\[ p - 8 = 9 \]

### Step 6: Solve for \( p \)
Now, add 8 to both sides to solve for \( p \):

\[ p = 9 + 8 \]

Thus,

\[ p = 17 \]

### Final Answer
The value of \( p \) is \( 17 \).

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