Solve the following equations by trial - and - error method .
6p - 2 = 3p + 13

Answer

To solve the equation \( 6p - 2 = 3p + 13 \) using the trial-and-error method, we will follow these steps:

### Step 1: Rearranging the equation
We start with the equation:
\[ 6p - 2 = 3p + 13 \]

### Step 2: Isolate the variable on one side
We can rearrange the equation to get all terms involving \( p \) on one side and constant terms on the other side. We do this by subtracting \( 3p \) from both sides:
\[ 6p - 3p - 2 = 13 \]

### Step 3: Simplify the equation
This simplifies to:
\[ 3p - 2 = 13 \]

### Step 4: Add 2 to both sides
Next, we add 2 to both sides to isolate the term with \( p \):
\[ 3p = 13 + 2 \]

### Step 5: Simplify further
This simplifies to:
\[ 3p = 15 \]

### Step 6: Divide by 3
Now, we divide both sides by 3 to solve for \( p \):
\[ p = \frac{15}{3} \]

### Step 7: Calculate the value of \( p \)
This gives us:
\[ p = 5 \]

### Final Answer
Thus, the solution to the equation \( 6p - 2 = 3p + 13 \) is:
\[ p = 5 \]

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