Chapter 8, Problem 6PSQ

To determine

To solve:

The given equation. Check your solution.

Answer to Problem 6PSQ

The solution of our given equation would be $f=-11$ .

Explanation of Solution

Given:

An equation:

  $29+4(f+2)=-7$ .

Calculation:

To solve our given equation, we use opposite operations as shown below:

  $\begin{array}{l}29+4(f+2)=-7\left(\text{Given equation}\right)\\ 29-29+4(f+2)=-7-29\left(\text{Subtracting 29 from both sides}\right)\\ 4(f+2)=-36\\ \frac{4(f+2)}{4}=\frac{-36}{4}\left(\text{Dividing both sides by 4}\right)\\ f+2=-9\\ f+2-2=-9-2\left(\text{Subtracting 2 from both sides}\right)\\ f=-11\end{array}$

Let us verify our answer by substituting $f=-11$ in our original equation.

  $\begin{array}{l}29+4(f+2)=-7\left(\text{Given equation}\right)\\ 29+4(-11+2)=-7\left(\text{Substituting }f=-11\right)\\ 29+4(-9)=-7\\ 29-36=-7\\ -7=-7\end{array}$

Since both sides of equation are equal, therefore, $f=-11$ is a solution of our given equation.