Chapter 3.2, Problem 23PPE

To determine

The solution of given inequality $-\frac{3}{4}>r-\frac{3}{4}$ . Graph and check the solutions.

Answer to Problem 23PPE

  $r<0$

  

Explanation of Solution

Given information:

The given inequality is $-\frac{3}{4}>r-\frac{3}{4}$ .

Calculation:

Add $\frac{3}{4}$ on both the sides.

  $\begin{array}{c}-\frac{3}{4}+\frac{3}{4}>r-\frac{3}{4}+\frac{3}{4}\\ 0>r\\ r<0\end{array}$

Here, the open circle is used because the inequality is “less than” $(<)$ . The black arrow is drawn to the left of the point  $0$ because these are the values that are less than $0$ .

  

To check the inequality, select any number which is less than $0$ .

Substitute the value of $r=-1$ in the given inequality $-\frac{3}{4}>r-\frac{3}{4}$ .

  $\begin{array}{l}-\frac{3}{4}\stackrel{?}{>}-1-\frac{3}{4}\\ -\frac{3}{4}>-\frac{7}{4}\end{array}$

The above condition is true.

Hence, the solution of the given inequality is all the real number less than $0$ i.e. $\left(r<0\right)$ .