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Solving Linear Inequalities

on the TI-89

Entering an Inequality:

You can enter an inequality on the TI-89 just as you would enter an equation. The "<" symbol is entered by pressing <2nd> "0", and the ">" symbol is entered by pressing <2nd>".". You may have already noticed these symbols on the calculator. It isn't shown on the calculator face, so you may not known that you can enter "<=" by pressing <Diamond>"0", and ">=" by pressing <Diamond>".". You can also access these operators using the Math Test menu (<2nd><5><8>).

Using solve():

Here are some screen shots of a solution to problem A1.26 (on p. A8) in the Larsen text, which says in part: "Solve the inequality 3x + 1 >= 2x + 2."

After selecting NewProb from the "F6 - Clean Up" menu, select "1: solve(" from the "F2 - Algebra" menu.

the algebra menu

Next, type the inequality, ",", then the variable you wish to solve for, and ")" <ENTER>. The solution is x >= 1 in interval notation.

solving an inequality

This screen shot shows you how to access the inequality operators from the Math Test menu (<2nd><5><8>) instead of the keyboard, if you prefer.

Math Test menu

A "Manual" Method:

Here is a "manual" solution to the same problem. This method can be useful in locating an error in paper-and-pencil work. After typing the problem, the solution proceeds by subtracting 2x from both sides (type "-", "2", "x", <ENTER>), then subtract 1 from both sides (type "-", "1", <ENTER> - the "ans(1)" is supplied automatically by the calculator.

Solving a linear inequality

Double Inequalities:

Look at problem A1.28 on p. A8 of the Larsen text. It says, in part "solve the inequality 0 <= x + 3 < 5" - let's pretend that it isn't trivial. The TI-89 won't manipulate a "double inequality" like this directly, you need to separate it into two separate inequalities as shown on the right. Of course, you still have to interpret the answer.

solving a double inequality

last update November 26, 2006 by JL Stanbrough