Chapter 4.5, Problem 2AGP

To determine

To solve and check: the given equation

Answer to Problem 2AGP

The required solution is $n=-21$

Explanation of Solution

Given: $8=15+\frac{n}{3}$

Calculation:

  $\begin{array}{l}8=15+\frac{n}{3}\text{ Write the equation}\\ 8-15=15+\frac{n}{3}-15\text{ Use subtraction property of equality}\\ -7=\frac{n}{3}\text{ Simplify }\\ \text{3}\text{.}\left(-7\right)\text{= 3}\text{. }\frac{n}{3}\text{ Use division property of equality}\\ -21=n\text{ Simplify}\end{array}$

Check by substituting the value of n to the original equation.

  $\begin{array}{l}\text{ 8}=15+\frac{n}{3}\text{ Write the equation}\\ 8=15+\frac{-21}{3}\text{ Substitute the value of }n\\ \text{ 8}=15+\left(-7\right)\text{ Simplify }\\ \text{ 8 =8 The statement is true}\end{array}$

Conclusion:

Therefore, the required solution is $n=-21$