Question

For Exercises 57-60, use the following information.

You can use the operators in the LOGIC menu on the Ti-83 Plus to graph compound and absolute value inequalities. To display the LOGIC menu, press$\boxed{2\text{nd}}\boxed{\text{TEST}}\boxed{}$.

A graphing calculator can also be used to solve absolute value inequalities. Write the expression you would enter for Y1 to find the solution set of the inequality$\left|2x-6\right|>10$. Then use the graphing calculator to find the solution set. (Hint: the absolute value operator is item 1 on the MATH NUM menu.)

Short answer

The required expression represented by $2x-16$and solution set is $\left\{x|x>8\text{or}x<-2\right\}$.

Step-by-step solution

Step 1- Write the required expression

The first expression will be derived from the inequality$2x-6>10$ that will be $2x-16$.

– Use the graphing calculator 

Insert the expression $2x-16$ in Y1 and $2x+4$ in Y2 by using the “abs(“ for each expression press the GRAPH button.

Step 3- Make the conclusion 

Use the TRACE button and arrow keys to find the points where the lines are touching the x-axis which are $8.510683$ and $-2.553191$ where the first value representing the Y1 and second representing the Y2 which represents that the solution set is $\left\{x|x>8\text{or}x<-2\right\}$.