Question

solving inequality: one third of a number increased to half this number is at least 3 less than that same number help.

Answer 1

Let the number = x

one-third of a number = 1/3 x

half the number = 1/2 x

at least means ≥

3 less than the same number: x - 3

so, the expression for the inequality will be:

`(1)/(3)x+(1)/(2)x\ge x-3`

Solve for x:

`\begin{gathered} (1)/(3)x+(1)/(2)x-x\ge-3 \\ -(1)/(6)x\ge-3 \\ \\ x\le3\cdot6 \\ x\le18 \end{gathered}`

So, the answer will be :

`\begin{gathered} x\le18 \\ x\in(-\infty,18\rbrack \end{gathered}`