Linear Inequalities Exercise - I

Page # 4 LINEAR INEQUALITIES EXERCISE - I UNSOLVED PROBLEMS Q.1 Draw the graphical solution of each of the following inequations : (i) x>3 (ii) x  1 (iii) x  – 2 (iv) x < 5 (v) x > – 2 (vi) x < – 3 Q.2 Draw the graphical solutions of each of the following inequations : (i) y  0 (ii) y > 3 (iii) y < –2 (iv) y  1 Q.3 Q.4 Q.5 Q.6 Q.7 Q.8 Q.9 Draw the graphical solutions of each of the following inequations : (i) |x| > 2 (ii) |x|  3 (iii) |y|  1 1 (iv) |y| < 3 (v) | 3x  2 | 2 1 7 (vi) | x  |  (vii) |x+1|  3. 4 4 Draw the graphical solutions of each of the following inequastions : (i) |x–1|>2 (ii) |y+3|5 (iii) |x–2|3 1 (iv) |y–1|<4 (v) |3x–2| 2 1 7 (vi) | x  |  (vii) |x+1|3. 4 4 Draw the graphical solution of each of the following system of inequation: (i) x  3, y < –2 (ii) x < 3, y > – 4, y < 2 (iii) |x|  1; |y|  1 (iv) |x–3| < 2; |y+2|  5 (v) x > 3, y  5, x  –2, y  7 Draw the graph of each of the following inequations: (i) x+y < 6 (ii) 3x–4y  12 (iii) 2x–4y  1 (iv) y–x  0 (v) 5x–2y < 10 (vi) x–2y  –1 (vii) x  8 – 4y Draw the graphical solution of each of the following system of inequation : (i) 2x+y < 2, x–3y  6. (ii) 3x+4y  12, 4x+3y  12, x  0, y 0 (iii) 2x+y  2, x–y  1, x+2y 8,x  0,y  0 (iv) |y–x|  3 (v) x+2y  0, 2x + y  4, x  0, y  2 (vi) 6x+5y  150, x+4y  80, x  15, x  0, y  0 Draw the graphical solution of each of the following: (i) x  0, x   6, y  0, y  7. (ii) x  0, y  0, x  y, x+y  6. (iii) x  5, y  3, x  y, x+2y  6 (iv) y  –4, y  4, x+2y  2, x–y  6 (v) x  2, x  8, y  x+3, 2x+y  10, y  4 (vi) 3x+2y  24, x + 2y  16, x + y  10, x  0, y  0. Draw the graphical solution of each of the following: (i) (iii) (iv) (v) y x x x < 0, 3x – y  0, y  5, x  4, y  – 3, + y > 6, 2x  0 (ii) x  0, x–y  0 – y  6. x + y  6 – y > 0 Q.10 Solve: 11x < 101 when (i)x is a natural number (ii) x is an integer. Q.11 Solve of: 3x–4  –2x + 6 when (i) x is a natural number (ii) x is a real number. 1 3  1 x  4   (x  6). Q.12 Solve for x: 2  5  3 Q.13 Solve for x: |x| < 4. Q.14 Solve: |3x–7|  2. x 5 0 Q.15 Solve for x: x2 Q.16 A recharger manufacturing company produces rechargers and its cost function for a week 1 is C(x) = 10 (4270 + 23x) and its revenue function is R (x) = 3x, where x in the number of rechargers produced and sold per week. How many rechargers mus be sold for the company to make a profit. Q.17 To receive grade A in a subject, one must obtain an average of 90 or higher marks in five examinations. If a student’s marks in the first four examinations are 91, 88, 93 and 95, find the minimum marks, a student must obtain to get grade A in the subject. Q.18 Solve the following inequations and represent the solution on the number line. 4  3x 2x  5 x3  5 (iii) 5 4 x 5 Q.19 Solve the following inequations and represent the solution on the number line. (i) 8x–2  5x+1 (ii) 4x  5 5 2(3  x) 9 1  (iii)  (ii) 3 3 5 5 2 Q.20 I.Q of a person is given by formula M.A.  100 where M.A. stands for mental I.Q. = C.A. age and C.A. stands for chronological age. If 75  I.Q.  135 for a group of 9 year children. Find the range of their mental age. (i) |3x–2|< ANSWER KEY 10. 11. 12. 14. 15. 16. (i) 1,2,3, ....., 9 (ii) ....–4,–3,–2,–1,0,1,2,...9 (i) 2,3,4, ..... (ii) {x  R/x  2}. {x  R/x  120} 13. –4 < x < 4. {x  R/x  5/3, x  3}. {x  R/–2 < x <5} 610 17. 83