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Mathematics Question on linear inequalities

If rr is a real number such that ∣r∣<1|r| < 1 and if a=5(1−r),a=5(1-r), then

A

0<a<50 < a < 5

B

−5<a<5-5 < a < 5

C

0<a<100 < a < 10

D

0≤a<100\le a<10

Answer

0<a<100 < a < 10

Explanation

Solution

∵\because ∣r∣<1|r| < 1
⇒\Rightarrow −1<r<1-1 < r < 1
Also, a=5(1−r)a=5(1-r)
⇒\Rightarrow 0<a<100 < a < 10
(∵at r=−1, a=10 and at r=1, a=0 )\left( \begin{aligned} & \because at\,r=-1,\,a=10 \\\ & and\,at\,r=1,\,a=0 \\\ \end{aligned} \right)