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

Page 41

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

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Contents EL-9650/9600c/9450/9400 Contents Always read Before Starting Read this firstIntroduction Using this HandbookSlope and Intercept of Linear Equations Enter the equation y = x for Y2 Parallel and Perpendicular Lines 2View the graphs Slope and Intercept of Quadratic Equations 1Change the equation in Y2 to y = x 2+2 Shifting a Graph of Quadratic Equations 1Move the graph y = x 2 to the right by 1Access the Solver feature This screen will appear a few 4Enter the values L=15,000, I=0.09, N=48 Access the Solver feature 200 15π 10π1Access the Solver feature 5Solve for the height and enter a starting point Graphing Polynomials and Tracing to Find the Roots 1Move the tracer near the left-hand root Graphing Polynomials and Jumping to Find the Roots EL-9650/9600c/9450/9400 Graphing Calculator Solving a System of Equations by Graphing or Tool Feature 1Access the Tool menu. Select the number of variables Entering and Multiplying Matrices Enter a 3 x 3 matrix B Solving a System of Linear Equations Using Matrices 17 0.83 = 0.5 0.5 17 0.17 Solving Inequalities 1Enter y = 34 2x for Y1 and y = 5 x for Y2 2x 5 ≥ Solving Double Inequalities= 2x 5 and y = 7 intersect at 6,7 + y ≤ System of Two-Variable Inequalities+ y ≥ Graphing Solution Region of InequalitiesContinuing key operations omitted If x ≥ Slope and Intercept of Absolute Value Functions3View the graph Shifting a graph of Absolute Value Functions = x y = Solve an absolute value equation 5 4x = Solving Absolute Value EquationsSolving Absolute Value Inequalities = -4, y = 2Set up shadingEvaluating Absolute Value Functions Evaluate Graphing Rational Functions + 1x Solving Rational Function Inequalities = y 2 + 2 = y = +- √ x + Graphing Parabolas1Change to parametric mode Graph x 2 2x + y 2 + 4y = Graphing Circles3Turn off Y1 so that it will not graph Graphing Ellipses View the graph in the new window Graphing Hyperbolas Zoom out the screen Key pad for the Sharp EL-9650/9600c Calculator Key pad for the Sharp EL-9450/9400 Calculator We thank you for your cooperation in this project Step Sharp Corporation OSAKA, Japan
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EL-9650, EL-9600c, EL-9400 specifications

The Sharp EL-9400 and EL-9450 are advanced programmable scientific calculators designed for professionals and students alike. Renowned for their versatile functionality and user-friendly interface, these calculators are popular in the fields of engineering, mathematics, and the sciences.

One of the hallmark features of the EL-9400 and EL-9450 is their extensive range of built-in functions. These calculators allow users to perform a variety of mathematical operations, including basic arithmetic, statistical calculations, complex number operations, and calculus functions. They support both decimal and fraction calculations, making them suitable for diverse mathematical applications.

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With their advanced graphing capabilities, these calculators allow users to plot functions and analyze their behavior over a defined range. The graphing feature is user-friendly, offering options to zoom in and out, providing a better understanding of mathematical concepts and aiding in visualization.

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Overall, the Sharp EL-9400 and EL-9450 stand out as powerful tools for anyone needing a reliable computing resource. Their combination of programmable features, comprehensive function sets, and user-friendly design makes them invaluable assets for students and professionals engaged in advanced mathematics and scientific calculations. With these calculators, users are equipped to tackle challenges and explore complex mathematical concepts with confidence.
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