Chapter 3.2, Problem 27PPE

To determine

The solution of given inequality $c-\frac{4}{7}<\frac{6}{7}$ . Graph and check the solutions.

Answer to Problem 27PPE

  $c<\frac{10}{7}$

  

Explanation of Solution

Given information:

The given inequality is $c-\frac{4}{7}<\frac{6}{7}$ .

Calculation:

Add $\frac{4}{7}$ on both the sides.

  $\begin{array}{c}c-\frac{4}{7}+\frac{4}{7}<\frac{6}{7}+\frac{4}{7}\\ c<\frac{6+4}{7}\\ c<\frac{10}{7}\end{array}$

Here, the open circle is used because the inequality is “less than” $(<)$ . The black arrow is drawn to the left of the point  $\frac{10}{7}$ because these are the values that are less than $\frac{10}{7}$ .

  

Substitute the end point $\frac{10}{7}$ into the equation $c-\frac{4}{7}=\frac{6}{7}$ .

  $\begin{array}{r}\frac{10}{7}-\frac{4}{7}\stackrel{?}{=}\frac{6}{7}\\ \frac{6}{7}=\frac{6}{7}\end{array}$

The above condition is true.

To check the inequality, select any number which is less than or equal to $\frac{10}{7}$ .

Substitute the value of $c=\frac{9}{7}$ in the given inequality $c-\frac{4}{7}<\frac{6}{7}$ .

  $\begin{array}{r}\frac{9}{7}-\frac{4}{7}\stackrel{?}{<}\frac{6}{7}\\ \frac{5}{7}<\frac{6}{7}\end{array}$

The above condition is true.

Hence, the solution of the given inequality is all the real number less than $\frac{10}{7}$ i.e. $\left(c<\frac{10}{7}\right)$ .