"Solving" an inequality means determining precisely which real numbers give a true statement when you substitute them for the variable in the inequality. The algebraic approach is the traditional approach, the one described in Stewart.

Example:     Solve the inequality x² - 3x + 3 <= 2x - 3.
                    (Netscape seems to have trouble with "less than or equal to" as one symbol.)
 

Pencil and Paper Procedure:

    First, subtract 2x - 3 from both sides of the inequality.
               You get (x² - 3x + 3) - (2x - 3) <= (2x - 3) - (2x - 3)
                or x² - 5x + 6 <= 0

    Next, factor.
               You get (x-2) (x-3) <= 0

    Finally, think about what it means for the product of two numbers to be negative.
                You get 2 <= x <= 3.

It's possible to get your calculator to do all the necessary algebra.

Calculator Procedures:

• Go to the HOME screen on your calculator and start a New Problem.
• Type in the inequality.
• We'll want to use the inequality again, so instead of hitting ENTER after you've typed in the inequality, store it.
• First, subtract 2x-3 from both sides. (If you stored the inequality in "i", enter i-(2x-3).)
• Next, factor the result.
• Finally, think about what it means for the product of two numbers to be negative. (The calculator will not do your thinking for you.)

1. Solve x² - 3x + 3 >= 3x - 3.
2. Solve 1/x <= 4. (You'll need to think about quotients rather than products. Be careful not to multiply by x during your calculations.)
3. Solve 3.217x² - 9.402x + 8.306 <= 7.841x - 6.669.
4. Solve 3.1x³ + 2.4x² - 1.3x - 0.7 < 0.

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