Chapter 6.3, Problem 66SR

To determine

To solve: the given equation and check the solution.

Answer to Problem 66SR

  $s=27$

Explanation of Solution

Given information:

Given solution

  $18=\frac{2}{3}s$

Calculation:

If each side of an equation is multiplied by the same nonzero number, the two sides remain equivalent.

For numbers $a,b$ and $c$ , where $c\ne 0$ , if $a=b$ ,then $ac=bc$

  $\begin{array}{c}18=\frac{2}{3}s\text{Write}\text{the}\text{equation}\\ \text{18}\left(\frac{3}{2}\right)=\frac{2}{3}s\left(\frac{3}{2}\right)\text{Multiplication}\text{property}\text{of}\text{Equality}\\ \cancel{\text{18}}\left(\frac{3}{\cancel{2}}\right)=\frac{2}{3}s\left(\frac{3}{2}\right)\text{Multiplication}\text{inverse}\text{property,}\frac{\text{2}}{\text{3}}\text{g}\left(\frac{\text{3}}{\text{2}}\right)\text{=1}\\ \text{27=1s}\text{Identity}\text{property 1s=s;}\end{array}$

The solution is $s=27$ .

Now, check as shown:

To check that $27$ is the solution, replace $b$ with 27in the original equation.

  $\begin{array}{c}18=\frac{2}{3}s\text{Write}\text{the}\text{equation}\\ 18=\frac{2}{3}\left(27\right)\text{Replace}s=27\\ 18=\frac{2}{\cancel{3}}\left(\cancel{27}\right)\text{Multiplication}\text{property}\text{of}\text{Equality}\\ \text{18=18}\text{Which is true}\end{array}$