Which of the following number lines correctly represents 'p' if,
`p- (2p+5)- 5 (1- 2p) = 2(3+4p)- 3(p- 4)`

Options

A.
B.
C.
D.

Answer

To solve the equation \( p - (2p + 5) - 5(1 - 2p) = 2(3 + 4p) - 3(p - 4) \), we will follow these steps:

### Step 1: Expand and simplify both sides of the equation

**Left Side:**
1. Distribute the negative sign and the multiplication:
\[ p - 2p - 5 - 5 + 10p \]
This simplifies to:
\[ p - 2p + 10p - 5 - 5 = 9p - 10 \]

**Right Side:**
2. Distribute the multiplication:
\[ 2 \cdot 3 + 2 \cdot 4p - 3(p - 4) \]
This simplifies to:
\[ 6 + 8p - 3p + 12 = 5p + 18 \]

Now, we have the simplified equation:
\[ 9p - 10 = 5p + 18 \]

### Step 2: Move all terms involving \( p \) to one side and constant terms to the other side

3. Subtract \( 5p \) from both sides:
\[ 9p - 5p - 10 = 18 \]
This simplifies to:
\[ 4p - 10 = 18 \]

4. Add 10 to both sides:
\[ 4p = 28 \]

### Step 3: Solve for \( p \)

5. Divide both sides by 4:
\[ p = \frac{28}{4} = 7 \]

### Conclusion
The value of \( p \) is 7.