2022 Ch1 Inequalities BMQ Soln (RVHS)

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2022 Ch 1 Inequalities and Equations (Solutions to Tutorial and Assignment) 1 Solutions to Tutorial 1: Inequalities and Equations Basic Mastery Questions 1. (a)    2 2 3 3 0 3 3 0 3 3x x x x x            (b)    4 4 2 2 2 29 9 0 3 3 0 3 0 (since 3 0)x x x x x x             3 3 (from 1(a))x    (c) 3 3 3x x     (d) 1 2 1 2 or 1 2x x x         3x   or 1x  (e)   2 1 3 0x    Since   2 1 0x   for all real x, so   2 1 3 0x    for all real x x   (f)   22 2 4 0 1 3 0x x x       Since   2 1 0x   for all real x, so there is no real solution for x for   2 1 3 0x    (g) 5 1 2 0 1 2 2 1 2 3 1x x x x                 (h) 2 2e 2 e 2x x    (since 2e 0x  for all real x)   2 1ln e ln 2 2 ln 2 ln 2 ln 2 2 x x x x        (i) 0.5 0.5 0 0.5 0.5 ln 0.5 ln 0.5x x x      1 (since ln 0.5 0)x   (j) 3 5 5 3 or 3 5x x x         (k) 2 2 29 25 0 9 and 25 0x x x             0 3 3 and 5 5 0x x x x       3 or 3 and 5 5x x x       Taking intersection: 5 3 x    or 3 5 x  3 3 5 3 5

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2022 Ch 1 Inequalities and Equations (Solutions to Tutorial and Assignment) 2 2. 2 1 3 2 3 x x x    