Question

Solve: 24x < 100, when

1. x is a natural number.
2. x is an integer.

Answer 1

The given inequality is:

$24x<100$

⇒ $\frac {24x}{24} < \frac {100}{24}$ [Dividing both sides by same positive number ]

⇒ $x< \frac {25}{6}$

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$(i)$ It is evident that 1, 2, 3, and 4 are the only natural numbers less than $\frac {25}{6}$.
Thus, when x is a natural number, the solutions of the given inequality are 1, 2, 3, and 4.
Hence, in this case, the solution set is {1, 2, 3, 4}.

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$(ii)$ The integers less than $\frac {25}{6}$ are ….. –3, –2, –1, 0, 1, 2, 3, 4.
Thus, when x is an integer, the solutions of the given inequality are ….. –3, –2, –1, 0, 1, 2, 3, 4.
Hence, in this case, the solution set is {….. –3, –2, –1, 0, 1, 2, 3, 4}.