If `2gamma + 7 + 3 ( 5 -2 gamma) = 12,` then `gamma =` _____

Options

A. `1//6`
B. 11
C. `5//2`
D. 7

Answer

To solve the equation \( 2\gamma + 7 + 3(5 - 2\gamma) = 12 \), we will follow these steps:

### Step 1: Expand the equation
First, we need to distribute the \(3\) into the parentheses:
\[ 3(5 - 2\gamma) = 3 \times 5 - 3 \times 2\gamma = 15 - 6\gamma \]
Now, substitute this back into the equation:
\[ 2\gamma + 7 + 15 - 6\gamma = 12 \]

### Step 2: Combine like terms
Next, we will combine the terms involving \(\gamma\) and the constant terms:
\[ (2\gamma - 6\gamma) + (7 + 15) = 12 \]
This simplifies to:
\[ -4\gamma + 22 = 12 \]

### Step 3: Isolate the variable term
Now, we will isolate the term with \(\gamma\) by moving the constant to the right side:
\[ -4\gamma = 12 - 22 \]
This simplifies to:
\[ -4\gamma = -10 \]

### Step 4: Solve for \(\gamma\)
Now, divide both sides by \(-4\) to solve for \(\gamma\):
\[ \gamma = \frac{-10}{-4} = \frac{10}{4} = \frac{5}{2} \]

Thus, the value of \(\gamma\) is:
\[ \gamma = \frac{5}{2} \]

---