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Evaluate the following expression when a = -2, b = 4, c = -1 and d = 3: -(3)/(2)b + (1)/(4)(ac + bd2).

April 8, 2026Mathematics

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Answer

\frac{7}{2}

3.5

4 steps

Here's the solution to 5(b):

(b) Evaluate the following expression when $a = -2$ , $b = 4$ , $c = -1$ and $d = 3$ :

-\frac{3}{2}b + \frac{1}{4}(ac + bd^2)

Substitute the given values into the expression.
$-\frac{3}{2}(4) + \frac{1}{4}((-2)(-1) + (4)(3^2))$
Perform the operations inside the parentheses and exponents first.
$-\frac{3}{2}(4) + \frac{1}{4}(2 + (4)(9))$ $-\frac{3}{2}(4) + \frac{1}{4}(2 + 36)$ $-\frac{3}{2}(4) + \frac{1}{4}(38)$
Perform the multiplications.
$-6 + \frac{38}{4}$
Simplify the fraction and perform the addition.
$-6 + \frac{19}{2}$
To add these, find a common denominator.
$-\frac{12}{2} + \frac{19}{2}$ $\frac{-12 + 19}{2}$ $\frac{7}{2}$
The value of the expression is $\boxed{\frac{7}{2}}$ or $\boxed{3.5}$ .

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