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I have got some basic problem of finding the bounds of variables in the inequality.

For Example, For the following inequality:

$1≤a

How can we have we have:

$a≥1,b≥4,c≥7,d≥10,e≥13$ $\;and$ $\;e<=30 $

1 Answers 1

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Assuming all variables are integers. From the first inequality $1 \le a$ we see $a \ge 1$. From the second one, we get $1 \le b-2$, or equivalently $b > 3$. Since $b$ is an integer, we must have $b \ge 4$...

Can you do the rest?

UPDATE

Let's do another one. We proved $b \ge 4$ so from $b-2 < c-4$ we see $c > b+2 \ge 4+2 = 6$. In summary, $c > 6$, so $c \ge 7$ since $c$ is an integer.

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    Thank You. So $ c-4>=1$ then we should conclude $c>5$ then we have $c>=6$ why in answer we counter with $c>=7$ ? – 2017-02-02
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    The Second problem is we have the rule of addition as: $ If a ≤ b, $ $then$ $ a + c ≤ b + c $ $and$ $a − c ≤ b − c.$ So why we get $ 1≤b−2,$ or equivalently $b>3$ an not $b>=3$ ? – 2017-02-02
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    @MuhammadB for first question, see update. For second, you are right, but you are given $b-2 \ge a > 1$ which implies $b-2 > 1$, this is stronger than $b-2 \ge 1$... – 2017-02-02