Sharp EL-9650, EL-9400, EL-9600c manual Solving Absolute Value Inequalities

EL-9650/9600c/9450/9400 Graphing Calculator

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. Solve

20 - 65x

< 8 by rewriting the inequality so that the right-hand side of

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” using Rapid Window feature to solve Q1.

WINDOW EZ 3 ENTER *

3 ENTER *

3 ENTER *

Step & Key Operation	Display
(When using EL-9650/9600c)	(When using EL-9650/9600c)
*Use either pen touch or cursor to operate.

1-1Rewrite the equation.

1-2Enter y = 20 -

6x

- 8 for Y1.

5

Y=

MATH

B

*

5

*

2 0

—

a/b

6

5

X/ /T/n

*

*

— 8

1-3View the graph, and find the x-intercepts.

GRAPH

2nd F CALC 5 * ➞ x = 10, y = 0

2nd F CALC 5 * ➞ x = 23.33333334

y= 0.00000006 ( Note)

1-4Solve the inequality.

Notes

20 - 65x < 8

➞20 - 65x - 8 < 0.

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.

8-4