Solve : `21-3(a-7)=a+20`

Options

A. `5(3)/(13)`
B. `5(3)/(7)`
C. `5(1)/(7)`
D. `5(1)/(2)`

Answer

To solve the equation \( 21 - 3(a - 7) = a + 20 \), we will follow these steps:

### Step 1: Distribute the -3
First, we need to distribute the -3 across the terms inside the parentheses.

\[ 21 - 3(a - 7) = 21 - 3a + 21 \]

### Step 2: Combine like terms
Now, combine the constant terms on the left side.

\[ 21 + 21 - 3a = a + 20 \]
\[ 42 - 3a = a + 20 \]

### Step 3: Move all terms involving \( a \) to one side
Next, we will move all terms involving \( a \) to one side of the equation and the constant terms to the other side.

Subtract \( a \) from both sides:

\[ 42 - 3a - a = 20 \]
\[ 42 - 4a = 20 \]

### Step 4: Move the constant to the other side
Now, subtract 42 from both sides:

\[ -4a = 20 - 42 \]
\[ -4a = -22 \]

### Step 5: Solve for \( a \)
Now, divide both sides by -4 to solve for \( a \):

\[ a = \frac{-22}{-4} \]
\[ a = \frac{22}{4} \]
\[ a = \frac{11}{2} \]

### Final Answer
Thus, the solution to the equation is:

\[ a = \frac{11}{2} \quad \text{or} \quad 5.5 \]

---