`(2(p+3)-7)/4=(16-2(3-p))/6`
In the equation above , what is the value of p ?

Answer

To solve the equation \((2(p+3)-7)/4=(16-2(3-p))/6\), we will follow these steps:

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

\[ 12 \cdot \frac{2(p+3)-7}{4} = 12 \cdot \frac{16-2(3-p)}{6} \]

This simplifies to:

\[ 3(2(p+3)-7) = 2(16-2(3-p)) \]

### Step 2: Distribute on both sides
Now, distribute the terms inside the parentheses:

\[ 3(2p + 6 - 7) = 2(16 - 6 + 2p) \]

This simplifies to:

\[ 3(2p - 1) = 2(10 + 2p) \]

### Step 3: Expand both sides
Now, expand both sides:

\[ 6p - 3 = 20 + 4p \]

### Step 4: Move all terms involving \(p\) to one side
Subtract \(4p\) from both sides:

\[ 6p - 4p - 3 = 20 \]

This simplifies to:

\[ 2p - 3 = 20 \]

### Step 5: Isolate \(p\)
Add 3 to both sides:

\[ 2p = 23 \]

### Step 6: Solve for \(p\)
Now, divide both sides by 2:

\[ p = \frac{23}{2} \]

### Final Answer
Thus, the value of \(p\) is:

\[ p = 11.5 \quad \text{or} \quad p = \frac{23}{2} \]

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