Chapter 2.2, Problem 27P

a. Solve $-8=\frac{x+2}{4}$

b. Write the right side of the equation in part (a) as the sum of two fractions. Solve the equation.

c. Did you find the equation in part (a) or the rewritten equation easier to solve? Why?

To determine

To solve the given equation.

Answer to Problem 27P

  $x=-34$

Explanation of Solution

Given information :

  $-8=\frac{x+2}{4}$

Now we shall solve the equation.

We get,

  $\begin{array}{l}-8=\frac{x+2}{4}\\ -32=x+2\\ x=-32-2\\ x=-34\end{array}$

To determine

To write right side of the equation as the sum of two factors.

Answer to Problem 27P

  $\frac{x+2}{4}=\frac{x}{4}+\frac{1}{2}$

Explanation of Solution

Given information :

  $-8=\frac{x+2}{4}$

Here we may write $\frac{x+2}{4}$ as $\frac{x}{4}+\frac{2}{4}$

Hence it can be written as the sum of two factors.

Hence $\frac{x+2}{4}=\frac{x}{4}+\frac{1}{2}$

To determine

To determine if the given equation or the rewritten equation is easier to solve.

Answer to Problem 27P

It is easier to solve with one factor instead of sum of two factors.

Explanation of Solution

Given information :

  $-8=\frac{x+2}{4}$

Here we may write $\frac{x+2}{4}$ as $\frac{x}{4}+\frac{2}{4}$

Now solving with the sum of two factors would increase two steps in solving the given equation.

Whereas with one factor it can be solve easily with two steps.

Hence it is easier to solve with one factor instead of sum of two factors.