Chapter 3.3, Problem 61PPE

To determine

The other inequalities in the given pattern.

Answer to Problem 61PPE

The $a$ is solution of the pattern of inequalities $x<20,x<30,x<40$

Explanation of Solution

Given information:

The pattern of inequalities:

  $\frac{x}{2}<10,\frac{x}{3}<10,\frac{x}{4}<10,\dots$

Calculation:

Given that, a real number $a$ is a solution of the pattern of inequalities

  $\frac{x}{2}<10,\frac{x}{3}<10,\frac{x}{4}<10,\mathrm{..........}$ Now, multiplying the first inequality by 2, the second by 3, third by 4 and so on, one can get the another pattern of inequalities $x<20,x<30,x<40,\dots \dots \dots \dots \mathrm{..}$

Here, two patterns of inequalities $\frac{x}{2}<10,\frac{x}{3}<10,\frac{x}{4}<10,\dots$ and

  $x<20,x<30,x<40,\dots \dots \dots \dots .$ are equivalent.

Hence, $a$ is also a solution of the pattern of inequalities $x<20,x<30,x<40$