Exercise 1
Solve \(\displaystyle 24 x<100\), when
(i)
\(\displaystyle x\) is a natural number.
(ii)
\(\displaystyle x\) is an integer.
Not cross-checked
This solution has not been cross-checked against the answer printed in NCERT.
NCERT’s answer
(i)
\{$\displaystyle 1$, $\displaystyle 2$, $\displaystyle 3$, $\displaystyle 4$\} (ii) $\displaystyle \{\ldots-3,-2,-1,0,1,2,3,4$,
Divide by a positive number. Dividing both sides of an inequality by a positive number leaves the sense of the inequality unchanged.
\[24x < 100 \quad\Longrightarrow\quad x < \frac{100}{24} = \frac{25}{6} = 4\tfrac{1}{6}\]
(i)
The natural numbers smaller than \(\displaystyle \tfrac{25}{6}\approx 4.17\) are \(\displaystyle 1,\,2,\,3,\,4\).
(ii)
Every integer smaller than \(\displaystyle \tfrac{25}{6}\) qualifies, and these run downwards without end from \(\displaystyle 4\).
(i) \(\displaystyle \{1,2,3,4\}\) (ii) \(\displaystyle \{\ldots,-3,-2,-1,0,1,2,3,4\}\)