TECHNOLOGY EXTENSION Solving Inequalities With a Graphing Calculator
TECHN O LO G Y EX TEN SI O N
Solving Inequa lities W ith a Gra phing Ca lcula tor
Di sp l a y i n g a So l u t i o n
Some graphing calculators can be used to display the solution to an inequality in one variable.
To display the solution to 2x + 1 < 3x - 2, choose
the dot mode from the mode settings, and enter the inequality in the Y= editor as follows. You can enter the inequality symbol using the TEST menu.
Y1 = 2X + 1 < 3X - 2
Then, graph Y1 in the standard viewing window.
1. Using paper and pencil, solve the inequality algebraically and graph the solution.
2. Compare your graph from question 1 with the way the calculator displays the solution.
3. Using the TRACE instruction, find the values of x in the solution.
4. Describe how each of the following can be used to give a more accurate answer than you found in question 3. a) the ZOOM menu
b) the U key and the TABLE SETUP screen
c) changing the window variables
5. a) Using the TRACE instruction, find the value
of y for each value of x in the solution.
b) Explain why the graph of the solution does not lie on the x-axis.
6. Graph Y1 using the connected mode instead of the dot mode. Explain why the dot mode should be used.
7. a) Modify the inequality by changing the < symbol to . Display the solution on the calculator.
b) Does the graphing calculator distinguish between
< and ? Explain.
82 MHR ? Chapter 1
So l v i n g I n e q u a l i t i e s
8. Display the solution to each of
the following inequalities using a
graphing calculator. In your
notebook, sketch each display and
describe how it should be modified
to show the solution fully. State the
solution to each inequality.
a) 2x + 3 7 b) 3x - 1 < 8
c) 2x - 3 > -x d) 5x + 8 4x + 5
e) -4x + 2 -2 f) 3x + 2 5x - 6
g) 2(x - 3) 4x - 2
h) 3(x - 1) - x > 4(x + 1) - 1
i) 23x x - 1
j)
34x
+
23x
-
5
6
<
2(x
-
1)
k)
x-1 2
<
x-2 3
l)
3
+
x-3 6
x
m) x - 2 3x - 1
n) 4(x + 2) > 2(5 - x)
9. Some graphing calculators, such as the T I-92 and T I-92 Plus, have the capability to solve inequalities algebraically. If this type of calculator is available, use the solve function to solve the inequalities in question 8. T he inequality symbols are found in the test submenu.
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