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These are the solutions to the NSSCO past questions on Inequalities.
The TI-84 Plus CE shall be used for applicable questions.
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(1.) At least 5 means ≥ 5
It means that the minimum should be 5
(2.) At most 5 means ≤ 5
It means that the maximum should be 5
(3.) Just 5 means = 5
It means exactly 5 or equal to 5
(4.) More than 5 means > 5
(5.) Less than 5 means < 5
(6.) No more than 5 means ≤ 5
It should not be more than 5
It means 5 or less
(7.) No less than 5 means ≥ 5
It should not be less than 5
It means 5 or more
Rules of Inequalities
c, d, e are real numbers
$
(1.)\text{ If } c \lt d \text{ and } d \lt e, \text{ then } c \lt e \quad\dots\text{Transitive Rule} \\[3ex]
(2.)\text{ If } c \gt d \text{ and } d \gt e, \text{ then } c \gt e \quad\dots\text{Transitive Rule} \\[3ex]
(3.)\text{ If } c \lt d, \text{ then } d \gt c \\[3ex]
(4.)\text{ If } c \gt d, \text{ then } d \lt c \\[3ex]
(5.)\text{ If } c \lt d, \text{ then } -c \gt -d \\[3ex]
(6.)\text{ If } c \gt d, \text{ then } -c \lt -d \\[3ex]
(7.)\text{ If } c \lt d, \text{ then } \dfrac{1}{c} \gt \dfrac{1}{d} \\[5ex]
(8.)\text{ If } c \gt d, \text{ then } \dfrac{1}{c} \lt \dfrac{1}{d} \\[5ex]
(9.)\text{ If } c \lt d, \text{ then } (c + e) \lt (d + e) \\[3ex]
(10.)\text{ If } c \gt d, \text{ then } (c + e) \gt (d + e) \\[3ex]
(11.)\text{ If } c \lt d, \text{ then } (c - e) \lt (d - e) \\[3ex]
(12.)\text{ If } c \gt d, \text{ then } (c - e) \gt (d - e) \\[3ex]
(13.)\text{ If } c \lt d, \text{ and } e \gt 0; \text{ then } ce \lt de \\[3ex]
(14.)\text{ If } c \lt d, \text{ and } e \lt 0; \text{ then } ce \gt de \\[3ex]
(15.)\text{ If } c \gt d, \text{ and } e \gt 0; \text{ then } ce \gt de \\[3ex]
(16.)\text{ If } c \gt d, \text{ and } e \lt 0; \text{ then } ce \lt de \\[3ex]
(17.)\text{ If } c \lt d, \text{ and } e \gt 0; \text{ then } \dfrac{c}{e} \lt \dfrac{d}{e} \\[5ex]
(18.)\text{ If } c \gt d, \text{ and } e \gt 0; \text{ then } \dfrac{c}{e} \gt \dfrac{d}{e} \\[5ex]
(19.)\text{ If } c \lt d, \text{ and } e \lt 0; \text{ then } \dfrac{c}{e} \gt \dfrac{d}{e} \\[5ex]
(20.)\text{ If } c \gt d, \text{ and } e \lt 0; \text{ then } \dfrac{c}{e} \lt \dfrac{d}{e}
$