Q7. - Algebra 2

Question

Evaluate each expression if $\mathbf{a}\mathbf{=}\mathbf{-}\mathbf{9}\mathbf{,}\mathbf{b}\mathbf{=}\frac{\mathbf{2}}{\mathbf{3}}\mathbf{,}\mathbf{c}\mathbf{=}\mathbf{8}\mathbf{,}$ and $\mathbf{d}\mathbf{=}\mathbf{-}\mathbf{6}$.

7. $\frac{\mathbf{db}\mathbf{+}\mathbf{4}\mathbf{c}}{\mathbf{a}}$

Step-by-Step Solution

Answer

The value of $\frac{db+4c}{a}$ is $\mathbf{-}\frac{\mathbf{28}}{\mathbf{9}}$.

Step 1 – Description of step.

Substitute $\frac{2}{3}$ for b and $-4$ for d into $db$.

$\begin{array}{c}\left(-6\right)\cdot \frac{2}{3}=\frac{-12}{3}\\ =-4\end{array}$

Step 2 – Description of step.

Substitute $-6$ for $db$, $-9$ for $a$ and 8 for c.

$\frac{\left(-4\right)+4·8}{\left(-9\right)}$

Step 3 – Description of step.

Multiply 4 by 8 then add the obtained value to $-4$ in the numerator.

$\frac{\left(-4\right)+32}{\left(-9\right)}=-\frac{28}{9}$

Therefore, the value of $\frac{db+4c}{a}$ is $-\frac{28}{9}$.