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

N/3 + n/2 >= n - 3

2n/6 + 3n/6 >= n - 3

5n/6 >= n - 3

5n >= 6n - 18

-n >= -18

n <= 18

Answer 2

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.