Question

If $3 \leqslant 3t - 18 \leqslant 18$ , then which one of the following is correct ?
A) $15 \leqslant 2t + 1 \leqslant 20$
B) $8 \leqslant t < 12$
C) $8 \leqslant t + 1 \leqslant 13$
D) $21 \leqslant 3t \leqslant 24$
E) $t \leqslant 7$ or $t \geqslant 12$

Answer 1

Hint: If $a \leqslant px \leqslant b$ shows in a given data then we find the interval in which the value of $x$ varies. Using the different operations we get the result . We add some or subtract something on all the sides to get the required answer . It is important to know that if we divide all the parts by some negative value then the sign changes according to the question.

Complete step by step answer:
Form the given data $3 \leqslant 3t - 18 \leqslant 18$
First we add $18$ in all the parts and we get
$ \Rightarrow 3 + 18 \leqslant 3t - 18 + 18 \leqslant 18 + 18$
Calculate and get
$21 \leqslant 3t \leqslant 36$
Now we divide all the parts by $3$ , we get
Since $3$ is positive value then sign will remain same
$ \Rightarrow \dfrac{{21}}{3} \leqslant \dfrac{{3t}}{3} \leqslant \dfrac{{36}}{3}$
$ \Rightarrow 7 \leqslant t \leqslant 12$
Now again add $1$ in all the parts we get the required answer
$ \Rightarrow 8 \leqslant t + 1 \leqslant 13$
Therefore option (C) is correct.

Note:
We can solve the problem by using other operations. First we can divide all the parts by $3$ and then we get $1 \leqslant t - 6 \leqslant 6$. Now add $7$ in all the parts and get the required result easily. We used this shortcut method for multiple choice questions. From the answer we say that the value of $t$ lies between this interval.