Sharp EL9900 manual Solving Absolute Value Inequalities, = 10, y =

EL-9900 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”.
			WINDOW	(	)	5	ENTER	5	0	ENTER
				-

Step & Key Operation Display

1-1Rewrite the equation.

1-2Enter y = 20 -					6x	- 8 for Y1.
					5
						2 0
	Y=		MATH	B	1		—	a/b
6		X/ /T/n			5

— 8

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

GRAPH
			5	➞ x = 10, y = 0
2nd F	CALC
		5		➞ x = 23.33333334
2nd F	CALC
				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.

10-3