Nov. 17 Rational Inequalities
Transcript of Nov. 17 Rational Inequalities
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Inequality
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Rational Inequality
4. Test points within each interval between the critical values, to determine if the expression as a whole is positive or negative
1. Simplify the rational expression so that zero is on one side and the expression involving x is on the other side
2. Factor any quadratic expressions
3. Place critical numbers on a number lineCritical Numbers: the zeros, and the values that make the inequality undefined(nonpermissible values)
5. State the intervals that qualify as solutions to the inequality
< 0x 1 (x 2)(x + 3)
Example
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10 2 3 4 5 6 7 8 9 1012345678910
< 0x 1 (x 2)(x + 3)
Solve the inequality
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< 0
x 1 (x 2)(x + 3)The graph of y =
5
Solve:
>_ 0x2 2x 8
x 1
10 2 3 4 5 6 7 8 9 1012345678910
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x2 2x 8
x 1Graph of y =
7
>x
x 3
1
x + 2
10 2 3 4 5 6 7 8 9 1012345678910
Solve
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Absolute Value Inequality
Graph y = x Graph y = x
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Graph y = x + 5 What will graph of y = x + 5 look like?
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x 2 <_ 5Solve graphically
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x 2 <_ 5Solve algebraically
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x2
1+ <_ 3
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x2
1+ <_ 3Solve algebraically
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Exercise 28
questions 6 12