Chapter 1.8, Problem 17P

Tell whether the given number is a solution of each equation.

$\frac{2}{3}m+2=\frac{7}{3},\frac{1}{2}$

To determine

To determine whether the number $\frac{1}{2}$ is a solution of the equation:

  $\frac{2}{3}m+2=\frac{7}{3}$

Answer to Problem 17P

Yes, the number $\frac{1}{2}$ is a solution of given equation.

Explanation of Solution

Given:

  $\frac{2}{3}m+2=\frac{7}{3}$

Concept Used:

To check whether a number ‘ a’ is a solution of a equation substitute a for the variable and then check whether it make equation an identity, that is if both sides left and right become equal.

Calculation:

In order to determine whether the number $\frac{1}{2}$ is a solution of the equation:

  $\frac{2}{3}m+2=\frac{7}{3}$

Substitute $\frac{1}{2}$ for m in given equation, as

  $\begin{array}{c}\frac{2}{3}\left(\frac{1}{2}\right)+2=\frac{7}{3}\\ \Rightarrow \frac{\cancel{2}}{3}\left(\frac{1}{\cancel{2}}\right)+2=\frac{7}{3}\\ \Rightarrow \frac{1}{3}+2=\frac{7}{3}\\ \Rightarrow \frac{1+6}{3}=\frac{7}{3}\\ \Rightarrow \frac{7}{3}=\frac{7}{3}\end{array}$

Since, an identity $\frac{7}{3}=\frac{7}{3}$ is arrived. Thus, the number 3 satisfies the given equation.

Thus, the number $\frac{1}{2}$ is a solution of given equation.