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6 Cards in this Set
- Front
- Back
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Add and subtract inequalities |
Add only if sign is the same. a>b + c>d = a+c > b+d Subtract only if the sign is opposite. a>b - c<d = a - c > b - d Take the sign of the inequality you subtract from |
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Inequality squared or cubed, square root or cube root? |
Both parts not negative = can square Can also square root. If either side can be negative we can't do this. Can always cube or cube root both parts of an inequality |
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Multiply/divide inequalities |
If both sides of 2 inequalities are positive AND they have the same sign you can multiply. x<a and y<b, xy < ab If both sides of 2 inequalities are positive AND they have a DIFFERENT sign you can divide. x<a and y>b, x/y < a/b Final inequality takes sign of nimerstor. |
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Multiplying inequalities |
Positive # = keep sign Negative # = FLIP sign ***NEVER multiply, reduce an inequality by a variable if the variable could equal 0 or be negative*** |
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Solving quadratic inequalities |
Make a graph, solve for roots of x < means between the roots (below x axis) e.g. 1 < x < 3 > means outside the roots (above x axis) e.g. x < 1 OR x > 3 |
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Absolute value rules |
If x ≤ 0, |x| = -x We open up mod and multiply RHS by -1, e.g. |-5| = -(-5) = 5 ***this is different from just |x|=-2, if we don't know that x is 0 or negative this is impossible because distance can't be negative*** If x ≥ 0, |x| = x, e.g. |5|=5
|x| ≥ 0
√(x²) = |x|
|0| = 0
|-x| = |x|
|x-y| = |y-x| i.e. Distance between 2 points
|x|+|y| ≥ |x+y| gave the same sign, equal sign holds. E.g. |-5|+|-2| = |-5+ -2| When different signs, > holds. E.g. |-5|+|2| > |-5+ 2|, 7 > 3 When both gave the same sign, equal sign holds. E.g. |-5|+|-2| = |-5+ -2|When different signs, > holds. E.g. |-5|+|2| > |-5+ 2|, 7 > 3|x|-|y| ≤ |x-y|Equal sign holds when both have the same sign (xy > 0) AND when |x|≥|y|
|x|-|y| ≤ |x-y| n holds when both have the same sign (xy > 0) Equal sign holds when both have the same sign (xy > 0) AND when |x|≥|y| AND when |x|≥|y|
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