Solving Absolute Value Equations - Sharp EL9600C - Graphing Calculator Handbook

Solving Absolute Value Equations

The absolute value of a real number x is defined by the following:
|x| = x if x
-x if x
If n is a positive number, there are two solutions to the equation |f (x)| = n because there
are exactly two numbers with the absolute value equal to n: n and -n. The existence of two
distinct solutions is clear when the equation is solved graphically.
Example
Solve an absolute value equation |5 - 4x| = 6
Before There may be differences in the results of calculations and graph plotting depending on the setting.
Start
Return all settings to the default value or to delete all data.
Step & Key Operation
(When using EL-9600)
*Use either pen touch or cursor to operate.
1
Enter y = |5 - 4x| for Y1.
Enter y = 6 for Y2.
Y= B
MATH
*
n
X/ /T/ 6
ENTER
*
2
View the graph.
GRAPH
3
Find the points of intersection of
the two graphs and solve.
2
2nd F CALC
*
2
2nd F CALC
*
The EL-9600/9400 shows absolute values with | | just as written on paper by
using the Equation editor. The graphing feature of the calculator shows the
solution of the absolute value function visually.
8-3
0
0
1 5 — 4
*
EL-9600/9400 Graphing Calculator
Display
(When using EL-9600)
There are two points of in-
tersection of the absolute
value graph and the hori-
zontal line y = 6.
The solution to the equation
|5 - 4x|= 6 consists of the two
values -0.25 and 2.75. Note
that although it is not as intu-
itively obvious, the solution
could also be obtained by
finding the x-intercepts of the
function y = |5x - 4| - 6.
Notes