Solve the equations and check your answer in the case:
`p-(2p+5)-5(1-2p)=2(3+4p)-3(p-4)`

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 the equation
Start by expanding both sides of the equation.

**Left Side:**
\[ p - (2p + 5) - 5(1 - 2p) \]
This can be simplified as:
\[ p - 2p - 5 - 5 + 10p \]
Combine like terms:
\[ p - 2p + 10p - 5 - 5 = 9p - 10 \]

**Right Side:**
\[ 2(3 + 4p) - 3(p - 4) \]
This can be simplified as:
\[ 6 + 8p - 3p + 12 \]
Combine like terms:
\[ 6 + 12 + 8p - 3p = 18 + 5p \]

Now, the equation looks like:
\[ 9p - 10 = 18 + 5p \]

### Step 2: Move all terms involving \( p \) to one side
Subtract \( 5p \) from both sides:
\[ 9p - 5p - 10 = 18 \]
This simplifies to:
\[ 4p - 10 = 18 \]

### Step 3: Move constant terms to the other side
Add \( 10 \) to both sides:
\[ 4p = 18 + 10 \]
This simplifies to:
\[ 4p = 28 \]

### Step 4: Solve for \( p \)
Divide both sides by \( 4 \):
\[ p = \frac{28}{4} \]
This simplifies to:
\[ p = 7 \]

### Step 5: Check the solution
Substitute \( p = 7 \) back into the original equation to verify:
Left Side:
\[ 7 - (2(7) + 5) - 5(1 - 2(7)) \]
Calculating:
\[ 7 - (14 + 5) - 5(1 - 14) = 7 - 19 - 5(-13) = 7 - 19 + 65 = 53 \]

Right Side:
\[ 2(3 + 4(7)) - 3(7 - 4) \]
Calculating:
\[ 2(3 + 28) - 3(3) = 2(31) - 9 = 62 - 9 = 53 \]

Since both sides are equal, our solution is verified.

### Final Answer:
\[ p = 7 \]