Solve for : `gamma : 3 ( gamma - 4) - 5 ( gamma + 5) = -21`

Options

A. `-4`
B. `-7`
C. `-3`
D. `-8`

Answer

To solve the equation \( 3(\gamma - 4) - 5(\gamma + 5) = -21 \), we will follow these steps:

### Step 1: Distribute the terms
Distributing the terms inside the parentheses gives us:
\[ 3\gamma - 12 - 5\gamma - 25 = -21 \]

### Step 2: Combine like terms
Now, we combine the terms with \(\gamma\) and the constant terms:
\[ (3\gamma - 5\gamma) + (-12 - 25) = -21 \]
This simplifies to:
\[ -2\gamma - 37 = -21 \]

### Step 3: Isolate the \(\gamma\) term
Next, we isolate the \(\gamma\) term by adding 37 to both sides:
\[ -2\gamma = -21 + 37 \]
This simplifies to:
\[ -2\gamma = 16 \]

### Step 4: Solve for \(\gamma\)
Now, we divide both sides by -2 to solve for \(\gamma\):
\[ \gamma = \frac{16}{-2} \]
This simplifies to:
\[ \gamma = -8 \]

### Final Answer
Thus, the solution for \(\gamma\) is:
\[ \gamma = -8 \]