Chapter 8.6, Problem 1.18E

Solution

To check: The solution of the inequalities by using the table option in Ti-83.

By using the tables, it can be observed that the solution sets are correct.

Given information:

The given statement is: Check the solution by using the table option.

Explanation:

Consider the given inequality.

Step 1: Open ti-83 calculator, Press the button Y= and enter the given equation.

Step 2: Press the 2ND key then press WINDOW key.

Step 3: Press 2ND key, Press GRAPH Key then the below table will be displayed.

The combine table is shown below:

The solution for $\frac{2}{x-1}<x$ is $-1<x<1$ and $x>2$ .

  

The solution for $x+1>\frac{x+5}{x+2}$ is $-3<x<-2$ and $x>1$ .

  

The solution for $\frac{2x}{\left(x-2\right)\left(x+3\right)}<1$ is $x<-3,-2<x<2\text{ and }x>3$ .

  

The solution for $\frac{2x+2}{x-1}<x+1$ is $-1<x<1\text{ and }x>3$ .

  

The solution for $\frac{x^2+1}{x}<2x$ is $-1<x<0\text{ and }x>1$ .

  

The solution for $\frac{x-1}{x-2}<\frac{x+3}{x-1}$ is $1<x<2\text{ and }x>\frac{7}{3}$ .

  

By using the tables, it can be observed that the solution sets are correct.