Evaluate 8a-b(7+a) with Fractional Values: a=-1/2, b=2/13

To solve this problem, we'll follow these steps:

• Step 1: Identify the expression and the given values for $a$ and $b$.
• Step 2: Substitute the given values into the expression.
• Step 3: Simplify the expression to find the result.

Let's work through the solution:

Given the algebraic expression:
$8a - b(7 + a)$.

Substitute $a = -\frac{1}{2}$ and $b = \frac{2}{13}$ into the expression:

$8(-\frac{1}{2}) - \frac{2}{13}(7 + (-\frac{1}{2}))$.

Start by simplifying each part:
$8(-\frac{1}{2}) = -4$.

Then simplify $(7 + (-\frac{1}{2}))$:
$7 - \frac{1}{2} = 6\frac{1}{2} = \frac{13}{2}$.

Now substitute back:
$-4 - \frac{2}{13} \times \frac{13}{2}$.

Simplify the multiplication:
$\frac{2}{13} \times \frac{13}{2} = 1$.

Therefore, the expression simplifies to:
$-4 - 1 = -5$.

Thus, the solution to the problem is $-5$.