Solving Absolute Value Equations - Sharp EL-9650 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.
Starting
Return all settings to the default value and delete all data.
Step & Key Operation
(When using EL-9650/9600c)
*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-9650/9600c/9450/9400 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
EL-9650/9600c/9450/9400 Graphing Calculator
0
0
(When using EL-9650/9600c)
1 —
5 4
*
Display
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