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: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 [tex]\frac{x}{3}[/tex]Half that number is [tex]\frac{x}{2}[/tex]3 less than that same number is [tex]x-3[/tex]A third of a number increased by half that number is at least 3 less than that same number is written as,[tex]\frac{x}{3}+\frac{x}{2}\geq x-3[/tex][tex]\frac{2x+3x}{6}\geq x-3[/tex][tex]\frac{5x}{6}\geq x-3[/tex][tex]5x\geq 6x-18[/tex][tex]5x-6x\geq -18[/tex][tex]-x\geq -18[/tex][tex]x\leq 18[/tex]Therefore, all the numbers are less than and equal to 18.