Nonlinear Inequalities and the Pythagorean Theorem
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
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| 1. Put everything on the left hand side so that we have for example Quad > 0. |
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| 2. Factor and set equal to zero. |
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| 3. Solve and place answers on a number line. This will cut the number line into two or three regions. |
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| 3. Solve and place answers on a number line. This will cut the number line into two or three regions. |
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| 4. Pick a test value for each region and plug that test value into each of the factors. Put plusses or minuses over the region depending on whether the test values test positive or negative. |
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| 5. If the region has two plusses or two minuses the the region is positive. If the region has one of each then the region is negative. |
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| 6. If the inequality is "<" then include the negative regions. If the inequality is ">" then include the positive regions. |
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| 7. If the inequality is a less (greater) than or equal to then include the endpoints with solid dot and the interval [] If the inequality is a less (greater) than then do not include the endpoints by showing an open dot and the interval () |
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