Create functions from the left-hand and right-hand sides of the given inequality, then solve for the point of intersection.
1.67
Practice makes perfect
To solve the inequality by graphing, we first have to create functions using the inequality's left-hand and right-hand sides.
y=x+1 and y=12 log x
To enter them in your calculator, push Y= and write them in the first two rows.
With our functions entered, we can push GRAPH to draw them.
The windows settings do not show both intersection points, so let's push WINDOW and change the settings of the x-axis.
We can see that there are two points of intersection. To find those points, we can use the intersect option. Push 2nd and TRACE, then choose the list's fifth option. Now we have to select the two graphs and provide the calculator with a guess of where the intersection might be.
Notice that the calculator shows coordinates of only one intersection point. We need to repeat the process to find the other intersection point.
The graphs intersect at x≈ 1.67 and x≈ 11.91. Notice that we are looking for x-values where the graph y=12log(x) shows a greater y-value than x+1. From the graph, we see that this happens between the intersection points. Therefore, the solution to the inequality must be 1.67
