Question

Find all numbers such that a third of a number increased by half that number is at least 3 less than that same number.

Answer 1

Answer:

All the numbers are less than and equal to 18.

Step-by-step explanation:

To find : All numbers such that a third of a number increased by half that number is at least 3 less than that same number ?

Solution :

Let the number be 'x',

A third of a number is $\frac{x}{3}$

Half that number is $\frac{x}{2}$

3 less than that same number is $x-3$

A third of a number increased by half that number is at least 3 less than that same number is written as,

$\frac{x}{3}+\frac{x}{2}\geq x-3$

$\frac{2x+3x}{6}\geq x-3$

$\frac{5x}{6}\geq x-3$

$5x\geq 6x-18$

$5x-6x\geq -18$

$-x\geq -18$

$x\leq 18$

Therefore, all the numbers are less than and equal to 18.

Answer 2

The set of numbers such that a third of a number increased by half that number is at least 3 less than that same number are given as; x <= 18.

According to the question;

Let the numbers in question be represented as x.

In essence;

$\frac{x}{3} + \frac{x}{2 } \geqslant x - 3$

$\frac{5x}{6} \geqslant x - 3$

• 5x >= 6x - 18

• -x >= -18

• x <= 18

Therefore, the set of numbers such that a third of a number increased by half that number is at least 3 less than that same number are given as; x <= 18.

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