Sharp EL9900 manual Solving Absolute Value Equations, Solve an absolute value equation 5 4x =

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EL-9900 Graphing Calculator

Solving Absolute Value Equations

The absolute value of a real number x is defined by the following:

x =	x if x ≥	0
	-xif x ≤	0

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		Display	Notes

1Enter y = 5 - 4x for Y1. Enter y = 6 for Y2.

Y= MATH B 1 5 — 4

X//T/n ENTER 6

2View the graph.

GRAPH

3Find the points of intersection of the two graphs and solve.

2nd F CALC 2

2nd F CALC 2

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.

The EL-9900 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.

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Contents EL-9900 Contents Read this first Always read Before StartingUsing this Handbook IntroductionFractions and Decimals ExamplePie Charts and Proportions BeforeSlope and Intercept of Linear Equations 1Enter 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 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 10π 200 15 π1Access 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 = x 4 + x 3 5x 2 3x +Find the next root Solving a System of Equations by Graphing or Tool Feature 1Access the Tool menu. Select the number of variables Entering and Multiplying Matrices 1Multiply the matrices a and B together at the home screen Solving a System of Linear Equations Using Matrices 2Calculate B-1C Solving Inequalities EL-9900 Graphing Calculator = 2x 5 Solving Double Inequalities2x 5 ≥ = 2x 5 and y = 7 intersect at 6,7 + y ≤ + y ≤2x + y ≥ + 2y ≤ 1 x 2 + y ≥ + 2y ≤ 1 y ≤ +y ≥ 4 y ≥ 4 xContinuing key operations omitted Slope and Intercept of Absolute Value Functions If x ≥3View the graph Solving Absolute Value Equations Solve an absolute value equation 5 4x =Solving Absolute Value Inequalities = 10, y =2nd F Calc 2 x = = 9.999999999 Note Evaluating Absolute Value Functions +3 1+3Math Graphing Rational Functions + 1x Solving Rational Function Inequalities Graphing Parabolas = y 2 + 2 = y = +√ x +Change to parametric mode 2x + y 2 + 4y = Graphing CirclesGraph x 2 2x + y 2 + 4y = 2x + y+22 =For Y1 = Y1 2 for Y2, and y = -Y1 -2 for Graphing Ellipses View the graph Graphing Hyperbolas Zoom out the screen Key pad for the Sharp EL-9900 Calculator Key pad for the Sharp EL-9900 Calculator Sharp Graphing Calculator Step Sharp Corporation OSAKA, Japan