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

EL-9650/9600c Graphing Calculator

Solving Inequalities

To solve an inequality, expressed by the form of f (x) ≤ 0, f (x) ≥ 0, or form of f (x) ≤ g (x), f (x) ≥ g (x), means to find all values that make the inequality true.

There are two methods of finding these values for one-variable inequalities, using graphical techniques. 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. For example, to find the solution to f (x) < 0, determine where the graph of f (x) is below the x-axis. The second method involves graphing each side of the inequality as an individual function. For example, to find the solution to f (x) < g (x), determine where the graph of f (x) is below the graph of g (x).

Example

Solve an inequality in two methods.

1. Solve 3(4 - 2x) ≥ 5 - x, by rewriting the right-hand side of the inequality as 0.

2. Solve 3(4 - 2x) ≥ 5 - x, by shading the solution region that makes the inequality true.

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

*Use either pen touch or cursor to operate.

1-1Rewrite the equation 3(4 - 2x) ≥ 5 - x so that the right-hand side becomes 0, and enter y = 3(4 - 2x) - 5 + x for Y1.

Y= 3 ( 4 — 2 X/ /T/n )

— 5 + X//T/n

1-2View the graph.

GRAPH

1-3Find the location of the x-intercept and solve the inequality.

2nd F CALC

5*

3(4 - 2x) ≥ 5 - x

➞3(4 - 2x) - 5 + x ≥ 0

The x-intercept is located at the point (1.4, 0).

Since the graph is above the x-axis to the left of the x-in- tercept, the solution to the in- equality 3(4 - 2x) - 5 + x ≥ 0 is all values of x such that

x ≤ 1.4.

7-1