Solve for `p - 5p - 6 = 8p - 4`

Options

A. `-1//3`
B. `-1//6`
C. `1//3`
D. `2//3`

Answer

To solve the equation \( p - 5p - 6 = 8p - 4 \), we will follow these steps:

### Step 1: Combine like terms on the left side
The left side of the equation is \( p - 5p - 6 \). We can combine the terms involving \( p \):

\[ p - 5p = -4p \]

So, the equation becomes:

\[ -4p - 6 = 8p - 4 \]

### Step 2: Move all terms involving \( p \) to one side
Next, we want to get all the \( p \) terms on one side. We can add \( 4p \) to both sides:

\[ -4p + 4p - 6 = 8p + 4p - 4 \]

This simplifies to:

\[ -6 = 12p - 4 \]

### Step 3: Move constant terms to the other side
Now, we will move the constant term \(-4\) to the left side by adding \( 4 \) to both sides:

\[ -6 + 4 = 12p - 4 + 4 \]

This simplifies to:

\[ -2 = 12p \]

### Step 4: Solve for \( p \)
Now, we can isolate \( p \) by dividing both sides by \( 12 \):

\[ p = \frac{-2}{12} \]

This simplifies to:

\[ p = -\frac{1}{6} \]

### Final Solution
Thus, the solution to the equation \( p - 5p - 6 = 8p - 4 \) is:

\[ p = -\frac{1}{6} \]

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