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Name: ____________________ Date: _______________ Unit 3 Review Packet (Spi.3.5 – all problems) Use the provided equations to solve for the variables listed below. Show all work for credit, using the methods that we have covered in class. 1. Solve for d: d e f c Answer: _________________________ 2. Solve for x: 3 x 12 Answer: _________________________ 3. Make a numbered list of all the things being done to f in the following equation. Write your answer in the space below. x d vrh kf e upg y _____ 4. Which of the following values of w would make the equation 3(4 w) 21 true? A. w = -4.5 B. w = -3 C. w = 3 D. w = 4.5 Name: ____________________ Date: _______________ ef a t for the variable f. On which line does he make a mistake? _____ 5. (a) Carlos is solving the equation x ef a t x x B. a ef a (tx) (a) A. x C. 1 1 ef tx (a) e e D. f tx (a) e (b) Show how Carlos’s problem should have been solved and write your answer in the answer blank. Answer: _________________________ _____ 6. Of which equations would a = -4 be a solution? I. 3a 5 5a 3 II. 2(a 3) 2 III. 4a 6 5a 2 A. B. C. D. E. I only II only III only I and II only I, II, and III 7. Describe how inverses are important in solving equations. You may use an example to help with your answer, but be sure to use sophisticated mathematical vocabulary in your response. __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ Name: ____________________ Date: _______________ 8. Explain why 8x – 6 + 7 = 5x + 3x + 1 has an infinite number of solutions (“all real numbers”). 9. Which of the following equations has no solution? I. 6(4 z 2) 3(8 z 4) II. 8t 3t 2 5t 6t III. 4x 1 13 A. B. C. D. E. I only II only III only I and II only I, II, and III 10. Temperature in America is typically measured in Fahrenheit, but most other countries use Celsius. To convert temperature from Celsius to Fahrenheit, you can use the formula 9 C 32 F , where C is degrees in Celsius and F is 5 degrees in Fahrenheit. a) Solve the formula for C. b) A science experiment is performed where a boiling liquid is measured at 45 C. Convert this into degrees Fahrenheit. 11. Solve for n: 32 7n 12 3n A. B. C. D. -5 5 6 9 12. Solve for n: 5x 2x 3 3x 10x A. B. C. D. 17/-6 14 21 No solution Name: ____________________ 13. Solve for p: 3 p 1 5( p 1) 2(7 2 p) A. B. C. D. Date: _______________ -10 -9 0 3 14. Sally takes the additive inverse of a number, then takes the multiplicative inverse of the new number, which results in -4. What was the original number? Answer : ____________________ 15. After simplifying av(r t w) , what will be the final coefficient of w? Answer : ____________________ Solve for x in the equations listed below. 16. wx k 17. r x h Answer: ____________________ Answer: ____________________ x z y 18. 19. ab x c Answer: ____________________ Answer: ____________________ a (c x) d 20. b 21. Answer: ____________________ Answer: ____________________ 22. 2x 4 5x 5 23. 2(3 x 4) 29 Answer: ____________________ Answer: ____________________ x mn y