mac1140_lecture11_1

mac1140_lecture11_1 - L11 2.7 Inequalities Solution sets...

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84 L11 §2 .7 Inequa l i t ie s Solution sets for inequalities are usually intervals of real numbers. Remember: When multiplying or dividing an inequality by a negative number, reverse the direction of the inequality sign. Example . Solve the linear inequality: 31 0 2 x + >− . 1. Open Intervals G raph In te rva l No ta t ion x a > axb << x b <
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85 2. Half-open G raph In te rva l Intervals No ta t ion x a axb ≤< 3. Closed Intervals ≤≤ 4. All real numbers () \ x −∞ < < +∞ Notes: 1) Solution sets to inequalities should be expressed in interval notation. 2) Express endpoints that are included by [ ] , and endpoints that are not included by ( ) . 3) Use to express ±∞ as “endpoints”. xb
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86 Example . Solve the linear inequality: 56 3 x x ≤− Example . Solve the three-part inequality : 3 4( 2 ) 5 2 x −≤ − <
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87 Introduction to Polynomial Inequalities (see page 305 in the textbook): Each polynomial of degree 1 or higher can be factored into a product of factors of the form ( ) m x k . x k = is called a zero of the polynomial. The exponent m is called the multiplicity of this zero. If the multiplicity is odd ( 1, 3, 5,. ..
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mac1140_lecture11_1 - L11 2.7 Inequalities Solution sets...

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