Question

Solve the following inequations.
1/2 x + 2 ≥ x - 1, where x ∈ N​

Answer 1

$\large\underline{\sf{Solution-}}$

Given:

$\sf\longmapsto \dfrac{1}{2}x+2 \geq x-1, x \in \mathbb{N}$

Multiplying both sides by 2, we get:

$\sf\longmapsto2\bigg( \dfrac{1}{2}x+2\bigg) \geq 2(x-1)$

$\sf\longmapsto x+4 \geq 2x-2$

$\sf\longmapsto x+4+-x\geq 2x-2-x$

$\sf\longmapsto 4\geq x-2$

$\sf\longmapsto 4+2\geq x-2+2$

$\sf\longmapsto 6\geq x$

$\sf\longmapsto x\leq 6, x\in\mathbb{N}$

Therefore:

$\sf\longmapsto x=\{1,2,3,4,5,6\}\ \ \red{Ans.}$