Evaluating the Algebraic Expression at x=2

The question requires finding the value of the expression $\frac{3(x + 7)}{2x - 1}$ when $x = 2$. This involves substituting the value of $x$ into the expression and simplifying.

Step 1: Substitute the value of x

Replace every instance of $x$ with the value $2$ in the given expression:

$ \frac{3(2 + 7)}{2(2) - 1} $

Step 2: Simplify the Numerator

Calculate the value of the numerator, $3(2 + 7)$:

• First, calculate the sum inside the parenthesis: $2 + 7 = 9$.
• Then, multiply by 3: $3 \times 9 = 27$.

The numerator is $27$.

Step 3: Simplify the Denominator

Calculate the value of the denominator, $2(2) - 1$:

• First, perform the multiplication: $2 \times 2 = 4$.
• Then, subtract 1: $4 - 1 = 3$.

The denominator is $3$.

Step 4: Calculate the Final Value

Divide the simplified numerator by the simplified denominator:

$ \frac{27}{3} $

$ \frac{27}{3} = 9 $

Therefore, the value of the expression $\frac{3(x + 7)}{2x - 1}$ when $x = 2$ is $9$. This corresponds to option B.