Chapter 1.1, Problem 45HP

To determine

To explain: the value of $k$ for the given equation.

Answer to Problem 45HP

The value of $k$ is $-12$ .

Explanation of Solution

Given information:

An equation is given as

  $4\left(\frac{k+6}{3}-12\right)+8=-48$

Calculation:

Consider the given equation.

  $4\left(\frac{k+6}{3}-12\right)+8=-48$

Now, solve for k as shown:

  $\begin{array}{c}4\left(\frac{k+6}{3}-12\right)+8=-48\\ 4\left(\frac{k+6}{3}-12\right)=-48-8\\ 4\left(\frac{k+6}{3}-12\right)=-56\\ \frac{4\left(\frac{k+6}{3}-12\right)}{4}=-\frac{56}{4}\\ \frac{k+6}{3}-12=-14\\ \frac{k+6}{3}-12+12=-14+12\end{array}$

Further simplify as shown:

  $\begin{array}{c}\frac{k+6}{3}=-2\\ 3\cdot \frac{k+6}{3}=-2\cdot 3\\ k+6=-6\\ k+6-6=-6-6\\ k=-12\end{array}$

Hence, $k=-12$ .