Draw the graphs of y= 12x-9 and y=2x. When does the first graph lie below the second graph?
{x|x> - 6 }
Practice makes perfect
To solve the given inequality using a graphing calculator, we need to treat each side of the inequality symbol as its own individual equation.
1/2x-9 <2x ⇒ ly=1/2x-9 y=2x
Then we can look for the values of x where the value of 12x-9 is less than the value of 2x. In other words, we want to find the values of x where the graph of y= 12x-9 lies below the graph of y=2x.
Graphing the Functions
Press Y= on the calculator to access the screen to input our functions.
To draw the graph, press the GRAPH button.
Finding the Solution Set
We see that the graphs intersect at a point. The x-coordinate of this point can be found by pressing 2ND and then CALC.
After selecting the intersect option, we choose the first and second curves. Then, the calculator asks for a guess where the intersection point might be. After that, it will calculate the exact point for us.
The lines intersect at x=-6. Tracing the lines on the calculator screen using the TRACE button, we can see that y= 12x-9 is the lower line after the intersection. Since the inequality is strict, it is not true at the point of intersection. This means that the given inequality holds true when x>-6.
1/2x-9< 2x
⇔
x>-6
We can now write the solution set for the inequality.
{x|x> - 6 }
