Draw the graphs of y=2(x-3) and y=3(2x+2). When does the first graph lie below the second graph?
{x|x> - 3}
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.
2(x-3) <3(2x+2)
⇓
ly=2(x-3) y=3(2x+2)
⇓
ly=2x-6 y=6x+6
Then we can look for the values of x where the value of 2x-6 is less than the value of 6x+6. In other words, we want to find the values of x where the graph of y=2x-6 lies below the graph of y=6x+6.
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=-3. Tracing the lines on the calculator screen using the TRACE button, we can see that y=2x-6 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>-3.
2x-6 < 6x+6
⇔
x>-3
We can now write the solution set for the inequality.
{x|x> - 3 }
