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

Solving Absolute Value Inequalities

To solve an inequality means to find all values that make the inequality true. Absolute value
inequalities are of the form |f (x)|< k, |f (x)| k, |f (x)|> k, or |f (x)| k. The graphical
solution to an absolute value inequality is found using the same methods as for normal
inequalities. 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. The second method involves
graphing each side of the inequality as an individual function.
Example
Solve absolute value inequalities in two methods.
1. 6x
Solve 20 -
5
the inequality is zero.
2.
Solve 3.5x + 4 > 10 by shading the solution region.
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.
Set viewing window to "-5< x <50," and "-10< y <10".
-
( )
WINDOW
Step & Key Operation
1
1
-
Rewrite the equation.
1
2
6x
-
Enter y = |20 -
5
Y= B 1
MATH
n
6 5
X/ /T/
— 8
1
3
-
View the graph, and find the
x-intercepts.
GRAPH
5
2nd F CALC
5
2nd F CALC
1
4
-
Solve the inequality.
< 8 by rewriting the inequality so that the right-hand side of
5 5 0
ENTER ENTER
| - 8 for Y1.
a /b
—
2 0
x = 10, y = 0
x = 23.33333334
y = 0.00000006 ( Note)
EL-9900 Graphing Calculator
Display
6x
|20 -
|20 -
The intersections with the x-
axis are (10, 0) and (23.3, 0)
( Note: The value of y in the
x-intercepts may not appear
exactly as 0 as shown in the
example, due to an error
caused by approximate calcu-
lation.)
Since the graph is below the
x-axis for x in between the
two x-intercepts, the solution
is 10 < x < 23.3.
Notes
|< 8
5
6x
| - 8 < 0.
5
10-3