Solving Inequalities - Sharp EL-9900 Handbook Vol. 1 Operation Manual

Solving Inequalities

To solve an inequality, expressed by the form of f (x)
f (x) g (x), means to find all values that make the inequality true.
There are two methods of finding these values for one-variable inequalities, using graphical
techniques. The first method involves rewriting the inequality so that the right-hand side of
the inequality is 0 and the left-hand side is a function of x. For example, to find the solution
to f (x) < 0, determine where the graph of f (x) is below the x-axis. The second method
involves graphing each side of the inequality as an individual function. For example, to find
the solution to f (x) < g(x), determine where the graph of f (x) is below the graph of g (x).
Example
Solve an inequality in two methods.
1.
Solve 3(4 - 2x)
2.
Solve 3(4 - 2x)
Before
There may be differences in the results of calculations and graph plotting depending on the setting.
Starting
Return all settings to the default value and delete all data.
Step & Key Operation
1
1
- Rewrite the equation 3(4 - 2x) 5 - x
so that the right-hand side becomes 0,
and enter y = 3(4 - 2x) - 5 + x for Y1.
3 (
Y= 4
+
—
5
X/ /T/
1
2
View the graph.
-
GRAPH
1
3
- Find the location of the x-intercept
and solve the inequality.
2nd F CALC
5
5 - x, by rewriting the right-hand side of the inequality as 0.
5 - x, by shading the solution region that makes the inequality true.
n
— 2 )
X/ /T/
n
EL-9900 Graphing Calculator
0, f (x) 0, or form of f (x)
Display
3(4 - 2x)
3(4 - 2x) - 5 + x
The x-intercept is located at
the point (1.4, 0).
Since the graph is above the
x-axis to the left of the x-in-
tercept, the solution to the in-
equality 3(4 - 2x) - 5 + x 0 is
all values of x such that
1.4.
x
g (x),
Notes
5 - x
0
9-1