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Algebra Name ____________________________ Instructor ______________ Hr/Blk __ Test 1 Review Solve each equation. 1. 6=p–8 2. m 4 7 3. 2j – 13 = 25 4. n 1 7 5 5. f 4 5 2 6. w 7 6 9 9 7. 4y – 16 + 8y = –4 8. -2(a + 6) = -22 9. 2x - 7 - (x - 5) = 10 10. 2(3x - 4) = -4(x + 7) Given the solution sets: Write in both set (-builder) and interval notation and then graph (if needed). 1. a is greater 4. 3. 2. No more than 10 people may use the treadmills at any time. 4. 5. Solve each inequality. Write in both set (-builder) and interval notation and then graph (if needed). 6. 2x + 7 < 20 7. -6x + 9 ≥ 21 8. x 4 2 5 9. 7 – 3x ≤ 2x + 6 10. 3(2c – 2) – 2c > 0 11. 3x – 5 > 4 or 9 - 2x > 5 12. -6 < 5m – 1 < 39 13. 6b – 1 ≤ 213 and 2b + 1 ≥ 11 Solve each equation / inequality. Graph the solution set. It is possible that the equation / inequality has no solution or all real numbers. 1. | x + 2 | = 11 2. | x + 16 | = 5 3. | 3x – 7 | = 5 4. | 8x + 2 | + 10 = 6 5. |x–9|>5 6. | 2x + 3 | < 5 7. | 7x – 4 | ≥ -38 8. | 7x – 4 | < -38 9. 12x – 23 = 1 + 4(3x – 6) 10. 8w – 5 > 2(4w – 3) . Define a variable and write an equation / inequality for each situation. Then solve. 1. Thirty decreased by the sum of a number and five equals one hundred. 2. A fair charges $7.25 for admission and $5.50 for a ride pass. Ten friends visited the fair. Not all of the friends purchased ride passes. If their total cost was $105.50, how many friends purchased ride passes? 3. Jasmine is 23 years old. Jasmine is 3 years less than half of George’s age. Find George’s age. 4. Three times a number plus 12 minus 5 times the same number is 22. What is the number? 5. Eli took the fleet of 8 vans for oil changes. All of the vans needed windshield wipers which cost $24 per van. The total bill was $432. Find the cost of an oil change. 6. Reliable Rentables rents a car for $12.95 per day plus 15¢ per mile. Your company has limited you to $90 a day for car rental. What is the maximum number of miles that you can drive each day? MULTIPLE CHOICE _____ 1. What value of x satisfies the equation -4x – 9 = -5 – 6x? A. -7 B. -1 C. 1 D. 2 E. 4 _____ 2. Solve for x: 2(x – 4) = 17 – 3x A. -4 9 B. 5 21 C. 5 D. 5 E. 25 _____ 3. What is the solution of the equation 3 (7x + 8) = -5 (4x + 9)? 69 41 53 41 15 41 1 41 A. B. C. D. E. 21 _____ 4. Which equation has no solution? A. | m – 4 | – 10 = 159 B. 6n – 1 = 12n + 2 C. 5w + 8 – w = 7w – 2(w – 4) D. 8 – (2v + 4) = 2v – 4 E. -2x + 3 – 8x = -10x – 3 _____ 5. Which of the following notations properly reflects the solution set below? A. B. C. D. E. { x | x < -7 or x > 14 } { x | -7 < x < 14 } { x | -7 > x > 14 } ( -7, 14 ] ( -∞, -7 ) U [ 14, ∞ ) _____ 6. What are the solutions of the inequality? A. x > - 7 x 2 5 Graph the solutions. B. x > - 7 C. x < -10 D. x > -10 E. none of the above _____ 7. Vis ordered concert tickets which were $3.50 for adults and $2.50 for students. She ordered 4 more student tickets than adult tickets. Her total bill was $56. How many of each did she order? What is the equation that represent the problem above? A. 3.50 (x) + 2.50 (4) = 56.00 B. 3.50 + 2.50 (x + 4) = 56.00 C. 3.50 (x) + 2.50 (x + 4) = 56.00 D. 3.50 (4) + 2.50 (x) = 56.00 E. 3.50 (x + 4) + 2.50 (x) = 56.00 _____ 8. Which graphs represents all of the solutions of –z + 7 < 3 ? A. B. C. D. E. none of the above _____ 9. A carpenter is cutting a 2 by 4 for the framing of a roof. The length needs to be 5 feet. He allows 0.1 foot possible variation for the length of the cut. What values of L represent the acceptable lengths for the board, in feet? A. L = 5 B. L > 4.9 C. L < 5.1 D. 4.9 < L < 5.1 E. L < 4.9 or L > 5.1 _____ 10. Which inequality represents the phrase all real numbers that are greater than -7 and less than -4? A. n > -7 B. n < -4 C. n > -7 or n < -4 D. -7 < n < -4 E. -4 < n < -7 _____ 11. Solve for x: 15 – 2x ≥ 55 A. x ≤ -40 B x ≥ -40 C. ( -∞, -20 ] D. [ -20 , ∞ ) E. none of the above _____ 12. What operation should you use to solve -6x = -24? A. add -6 to both sides B. add 6 to both sides C. subtract 6 from both sides D. multiply by 6 to both sides E. divide by -6 to both sides _____ 13. Solve for x: | 2x +10 | = 6 A. 2 B. -2, 2 C. -8, -2 D. -8, 2 E. no solution _____ 14. What are the solutions of 8 < x + 2 < 12? A. [ 6, ∞ ) B. [ 6, 10 ) C. [ 6, 14 ) D. [ 10, 14 ) E. [ -∞, 10 ) _____ 15. What is the solution of 2n – 3(4n + 5) = -6(n – 3) – 1? A. -8 B. -6 C. D. 1 4 E. 4 1 2 _____ 16. What are the solutions of | 5a + 5 | > 35? A. ( -∞, -8 ] B. [ -8, 6 ] C. [ 6, ∞ ) D. ( -∞, -8 ] U [ 6, ∞ ) E. ( -∞, ∞) _____ 17. A merchant is selling wind chimes from a booth at a flea market. He rents his space for $125 per day. The profit from each wind chime sold is $12. His goal is to make $3500 in a five day work week. Which equation represents how many chimes he needs to sell in a week to meet his goal? A. 12c – 625 = 3500 B. 5(12c) + 125 = 3500 C. 5(12c) – 125 = 3500 D. 5(12c + 125) = 3500 E. 5(12c – 125) = 3500 _____ 18. Which compound inequality represents the graph shown to the right? A. 7d + 1 < 0 B. 7d + 1 > 0 C. 7d + 1 < 1 or 7d + 1 > 15 D. 1 < 7d + 1 < 15 E. 1 < 7d + 1 < 15 _____ 19. ∣4x∣ + 3 < 0 3 A. x < 4 3 B. , 4 C. both A & B D. no solution E. all reals _____ 20. Which of the following solutions is true for A. B. 11 4 1 12 C. 0 D. E. 3 4 13 4 x 1 ? 3 4