Lial/Hungerford/Holcomb: Mathematics with Applications 11e Finite Mathematics with Applications 11e Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved. Chapter 1 Algebra and Equations Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved. Section 1.1 The Real Numbers Copyright ©2015 Pearson Education, Inc. All right reserved.

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Graph all real numbers x such that . Example: Graph all real numbers x such that . Solution: This graph includes all the real numbers between 1 and 5, not just the integers. Graph these numbers by drawing a heavy line from 1 to 5 on the number line. Parentheses at 1 and 5 show that neither of these points belongs to the graph. Copyright ©2015 Pearson Education, Inc. All right reserved.

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Copyright ©2015 Pearson Education, Inc. All right reserved. Section 1.2 Polynomials Copyright ©2015 Pearson Education, Inc. All right reserved.

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Copyright ©2015 Pearson Education, Inc. All right reserved. Example: Subtract: Solution: Eliminate parentheses. Group like terms. Combine like terms. Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved. Section 1.3 Factoring Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved. Example: Factor: Solution: We must find integers b and d such that Since the constant coefficients on each side of the equation must be equal, we must have that is, b and d are factors of 18. Similarly, the coefficients of x must be the same, so that The possibilities are summarized in this table: There is no need to list negative factors, such as because their sum is negative. The table suggests that 6 and 3 will work. Verify that Copyright ©2015 Pearson Education, Inc. All right reserved.

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Copyright ©2015 Pearson Education, Inc. All right reserved. Section 1.4 Rational Expressions Copyright ©2015 Pearson Education, Inc. All right reserved.

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Copyright ©2015 Pearson Education, Inc. All right reserved. Example: Divide Solution: Invert the second expression and multiply (division rule): Invert and multiply. Multiply. Lowest terms Copyright ©2015 Pearson Education, Inc. All right reserved.

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Exponents and Radicals Section 1.5 Exponents and Radicals Copyright ©2015 Pearson Education, Inc. All right reserved.

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Use the inversion property to compute each of the following. (a) (b) Example: Use the inversion property to compute each of the following. (a) (b) Solution: (a) (b) Copyright ©2015 Pearson Education, Inc. All right reserved.

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First-Degree Equations Section 1.6 First-Degree Equations Copyright ©2015 Pearson Education, Inc. All right reserved.

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Copyright ©2015 Pearson Education, Inc. All right reserved. Example: Solve Solution: First, simplify the equation by using the distributive property on the left-side term and the right-side term One way to proceed is to add to both sides: The solution is 2. Check this result by substituting 2 for k in the original equation. Copyright ©2015 Pearson Education, Inc. All right reserved.

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Copyright ©2015 Pearson Education, Inc. All right reserved. Section 1.7 Quadratic Equations Copyright ©2015 Pearson Education, Inc. All right reserved.

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Copyright ©2015 Pearson Education, Inc. All right reserved. Example: Solve Solution: Rewrite the equation as Now factor to get By the zero-factor property, the product can equal 0 only if Solving each of these equations separately gives the solutions of the original equation: Verify that both 1/3 and −3/2 are solutions by substituting them into the original equation. Copyright ©2015 Pearson Education, Inc. All right reserved.

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