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16 Cards in this Set
- Front
- Back
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When do you flip the sign of an inequality? |
When you multiply or divide an inequality by a negative number |
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How do you manipulate a compound inequality? e.g. x + 3 < y < x + 5 |
Must perform the operation on every term |
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For inequality with ranges, what should you use to solve? e.g. what could be the max value for xy if 0 < x < 3 and y< 8 |
Use the extreme value denoting LT or GT. e.g. LT3 * LT8 = LT24 |
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What is 15 - LT6 |
GT9 |
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What is 8 + LT2 |
LT10 |
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What is 8 * LT2 |
LT16 |
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What is 8 / LT2 |
GT4 |
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-7 * LT2 |
GT(-14) |
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LT8 * LT2 |
LT16 |
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What is the implication of xy > 0 |
They have the same sign, both neg or pos |
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What is the implication of xy < 0 |
They have diff signs, one neg and one pos |
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x² - x < 0 |
x² < x so 0 < x < 1 |
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What should you do if you take the square root of an inequality? e.g. x² < 4 |
Evaluate the absolute value so √x² < √ 2 => |x| < 2 |
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How do you solve an equation whith unknowns in the denominator? e.g. x/y < 1, is x < y |
Need to know the signs of both sides. You're NOT ALLOWED to multiply both sides of an equation without considering both cases of if it's positive or negative (as if negative you flip the sign). A DS trap. |
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How do you take the reciprocal of an inequality? e.g. 1/x < 1/y |
Need to know the signs of both sides. Cannot take the reciprocal of an inequality unless we know the sign. If we do know the sign, a negative number on both sides flips the sign if we take the reciprocal. A negative on one side doesn't. |
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How do you solve for an inequality with squares? E.g Is x^2 > y^2? 1. X>y 2. X>0 |
Need to know the signs of both sides.
If both sides are negative flip the inequality sign when you square.
If both sides are known to be positive, then don't flip the sign when you square.
If one side is positive and on negative you cannot square.
If the signs are unclear you cannot square. Don't know whether to flip.
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