By Laurie Boswell, Holt Mcdougal
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EXAMPLE 1 Assign labels. Write an algebraic model. Write an Algebraic Model You and some friends are at a Chinese restaurant. You order several $2 plates of wontons, egg rolls, and dumplings. 20. Use modeling to find how many plates you ordered. Student Help Solution STUDY TIP Be sure you understand the problem before you write a model. For example, notice that the tax is added after the cost of the plates is figured. 20 2 p ϭ 24 p ϭ 12 ANSWER ᮣ 36 Chapter 1 Connections to Algebra Write algebraic model.
5(y2 ϩ 4) Ϫ 7 4. 5x Ϫ 1 ϭ 3 ϩ x 5. 3x ϩ 2 ≤ 8 6. 5x > 20 7. Complete: An x value of 4 is a ____ ? of the equation x ϩ 1 ϭ 5, because 4 ϩ 1 ϭ 5. Skill Check Check to see if a ؍5 is or is not a solution of the equation. 8. a ϩ 8 ϭ 13 9. 27 ϭ 36 Ϫ 2a 10. a Ϫ 0 ϭ 5 11. 2a ϩ 1 ϭ 11 12. 6a Ϫ 5 ϭ 15 13. 5a ϩ 4 ϭ 26 14. 45 Ϭ a ϭ 9 15. a2 ϩ 2 ϭ 27 40 16. ᎏᎏ ϭ 8 a Check to see if b ؍8 is or is not a solution of the inequality. 17. b ϩ 10 > 19 18. 14 Ϫ b ≤ 3 19. 5b > 35 20. 8 ≥ 64 Ϭ b 21. 3b Ϫ 24 > 0 22.
Evaluate Exponential Expressions Evaluate the variable expression when s ؍2 and t ؍4. 10 Chapter 1 4. (t Ϫ s)3 5. (s 2) ϩ (t 2) 6. (t ϩ s)2 7. (t 2) Ϫ (s 2) 8. (s 2) ϩ t 9. 3 you will learn several rules for order of operations. One of those tells us that 2x3 is to be interpreted as 2(x3). Student Help READING ALGEBRA Notice that in part (a) of Example 4, the exponent applies to x, while in part (b), the exponent applies to 2x. 4 EXAMPLE Exponents and Grouping Symbols Evaluate the variable expression when x ϭ 4.