Multi-Step Inequalities Practice True False Questions Indicate True or False for the following Statements.

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1 Multi-Step Inequalities Practice True False Questions Indicate True or False for the following Statements. 1. There is no solution to the inequality 5x 2 8, given that x is a natural number. ( True/False ) 2. The solution for 16 2x 6 is x 11. ( True/False ) 3. x 2 > x + 5 for any positive number x. ( True/False ) 4. Solving the inequality 3(x 2) < 1 gives us x > 2. ( True/False ) 5. Inequalities can have infinitely many solutions, no solutions, or a finite set of solutions. ( True/False ) 6. The given inequality x 10 > x + 3 has no solution. ( True/False ) 7. The solution for 4.75x x is x 6 ( True/False ) 8. To solve any multistep inequality, one should remove any parentheses by using the distributive property and simplify each side of the inequality by combining like terms. ( True/False ) a 9. If a > b, then for a positive c: c < b c. ( True/False ) 10. Solving 3(5x + 2) > 5x + 16 gives x > 1. ( True/False ) 11. The solution for 2(x + 3) > 14 is x > 4. ( True/False ) 12. represents the solution of x 6 6. ( True/False ) 13. The graph of x < 3 is. ( True/False ) Short Answer Questions Fill in the answer blanks with correct answer. 14. Your company is given $100 to start off, and makes a $50 profit every week afterwards. Find the minimum number of weeks it will take you to have a profit of $375. weeks Answer: 15. You spend $7 to buy supplies for making lemon juice, and plan on selling every cup of lemon juice for $0.50. Find the minimum number of cups of lemon juice you have to sell in order to make a profit. cups of lemon juice Answer: 16. You spend $22 to buy supplies for making necklaces, and plan on selling them for $3 each. Find the minimum number of necklaces you have to sell in order to make a profit. necklaces Answer: 17. You spend $25 to buy supplies for making gloves, and plan on selling them for $5 each pair. Find the minimum number of gloves you have to sell in order to make a profit. pairs of gloves Answer: 18. You spend $11 to buy supplies for making socks, and plan on selling them for $2 each pair. Find the minimum number of socks you have to sell in order to make a profit. pairs of socks Answer: 19. Your friend invested $500 in his shop to start off, and makes a $20 profit every week afterwards. Find the minimum number of weeks it will take your friend to have a profit of $400. weeks Answer: 20. Your sister s store is given $200 to start off, and makes a $40 profit every week afterwards. Find the minimum number of weeks it will take your sister to have a profit of

2 weeks Answer: 21. You spend $20 to buy supplies for making milky tea, and plan on selling every cup of milky tea for $1. Find the minimum number of cups of milky tea you have to sell in order to make a profit. cups of milky tea Answer: Multiple Choice Questions For each question, four alternative choices are given, of which only one is correct. You have to select the correct alternative and mark it in the appropriate option. 22. Solve for x: 59 > 8x 5 x < 8 x > 8 x 8 x Graph the following inequality 3(x 1) Solve the multi-step inequality: 3(x 2) 4x + 3 x 9 x < 9 x < 9 x Find the solution set of 3x 2 > 19 or 3 2x 7; x belongs to R. x < 7 or x 5 x > 5 or x 5 x > 7 or x < 5 x > 7 or x 5

3 26. Solve the multi-step inequality: 2x 5 > 3x + 5 x < 10 x > 10 x < 10 x > Solution of the inequality 3x 4 > 11 is. x > 5 x > 5 x < 5 x < Represent the following inequality on the Real Number line: 2x 1 < Simplify the following inequality, then select the correct graph. 8x B) 30. Solve for x: 1 2 (x + 4) > 2(x 8) x > x > x > x > Graph the following inequality 3x 21 > x 11 3

4 32. Find the solution: 1 8 x 2 2( 1 4 x + 6) x 16 x 16 x 16 x Solve for x: 59 > 8x 5 x < 8 x > 8 x 8 x Simplify the following inequality, then select the correct graph. 7x + 4 < 11 4

5 35. Graph the following inequality 8x 19 5x Graph the following inequality 2(x + 4) < 10 A) 37. Graph the following inequality 6 5m < 8 7m 5

6 D) 38. Graph the inequality 3x 4 > Evaluate: 15x + 4 8x 17 x 5 x 3 x 3 x Identify the solution set of 7x > 2(x + 15). x > 6 x > 6 x < 6 None o f the above 41. Solve the multi-step inequality: 2(x 2) 6x 4 x < 0 x 0 x > 4 x Solve for x : 5x 3 < 3x + 1. x > 2 x < 2 x > 3 x Which set of values make the inequality 2x + 8 > 16 true? x = 4,5,6,7,8 x = 5,6,7,8,9 x = 3,4,5,6,7 x = 2,4,6,8, Solve for x : 6x x 3 x 3 x 3 x 3 6

7 45. Simplify the following inequality, then select the correct graph. 5x + 9 < Translate the following statement into an inequality Three more than two times x is less than seven 2(3 + x) < < 7 2x + 3 < 7 2x Solve the inequality 12 + ( 11x 6 ) 5 + 3x. x > 6 x < 6 x < 6 x Solve the multi-step inequality: 3x 2 x < x x < 7 x > Translate the following statement into an inequality Six times the sum of x and twelve is less than fourteen. 6(x + 12) < < 14 6x + 12 <14 6(x + 12) 14 7

8 50. Solve the inequality: 3x 7 3 x x 33 2 x 33 x 2 33 x Represent the following inequality on the Real Number line: 3x 6. None o f the above 52. Graph the following inequality 2 + 6m < -5 m 53. Graph the following inequality 5(x + 7) < 60 A) 8

9 54. Simplify the following inequality, then select the correct graph. 3x + 5 > Which set of values make the inequality 3x 2 < 22 true? x = 4,5,6,7,8 x = 5,6,7,8,9 x = 3,4,5,6,7 x = 2,4,6,8, Solve the multi-step inequality: 2(x 3) 11 4x 2 x > 6 11 x 3 10 x < x Graph the following inequality 6(x +2) 24 9

10 58. Graph the following inequality 6(x 5) 6 D) 59. Translate the following statement into an inequality The difference between eleven and four times x is greater than or equal to three 11 4x 3 (11 4)x x > 3 (11 4)x > Translate the following statement into an inequality The sum of seventeen and seven times x is greater than or equal to four x 4 (17+ 7)x x > 4 (17 + 7)x > Graph the following inequality 9x + 22 > 4x

11 62. Solve for x: 2 3 x x 12 x 12 x 12 x Which of these represents the solution on the number line for 5 2x 7. FIGURE 1 11

12 FIGURE 2 FIGURE 3 12

13 None o f the above 64. Solve the multi-step inequality: x 2 < 3x 12 x > 24 5 x > 5 24 x < 12 x Solve the multi-step inequality: 6x ( 2x x > 12 x 7 12 x < 7 x Simplify the following inequality, then select the correct graph. 6x ) 67. Evaluate: 1 4 x 5 < 3 x > 2 x < 2 x > 32 x < Solve the multi-step inequality: x 4 < 2x + 3 x < 12 7 x > 12 x > 12 7 x < Simplify the following inequality, then select the correct graph. 6x + 3 > 27 A) 13

14 70. List the solution set of 50 3(2x 5) < 25, given that x belongs to the set of Whole Numbers. (8, 9,...) (7, 8, 9,...) ( 7, 8, 9,...) None 71. Translate the following statement into an inequality The difference between three times x and 15 is greater than or equal to five 3x (x 15) 5 3x 1 > 5 3(x 15) > What is the solution set of 2y 3 < y + 1? y < 4 y > 4 y < 4 None o f the above 73. Graph the following inequality 8(x 1) > 8 A) 14

15 74. Graph the following inequality 4(x + 2) > Translate the following statement into an inequality Five less than four times x is less than or equal to sixteen 4x x - 5 < 16 5x + 4 < 7 4x Graph the following inequality 26 4m > 44 7m A) 15

16 77. Graph the following inequality 4(x + 6) 28 A) 78. Translate the following statement into an inequality The difference between fifteen and two times x is greater than eleven 15 2x 11 (15 2)x x > 11 (15 2)x > Simplify the following inequality, then select the correct graph. 2x D) Evaluate: 5x + 3 > 28

17 x > 6 x > 5 x > 4 x < Solve the multi-step inequality: 3 ( x 2 + 4) > 6(2x 3) x < 20 7 x 18 x 7 20 x > Translate the following statement into an inequality Five more than sixteen times x is less than or equal to six 5(16 + x) < < 6 16x + 5 < 6 16x Simplify the following inequality, then select the correct graph. 4x + 2 > Graph the following inequality 5x 12 3x 4 17

18 D) 18