# Solve: 4x − 2 < 8, when

Question:

Solve: 4x − 2 < 8, when

(i) x ∈ R

(ii) x ∈ Z

(iii) x ∈ N

Solution:

We have, $4 x-2<8$

$\Rightarrow 4 x<8+2$       (Transposing $-2$ to the RHS)

$\Rightarrow 4 x<10$

$\Rightarrow x<\frac{10}{4}$     (Dividing both the sides by 4 )

$\Rightarrow x<\frac{5}{2}$

(i) $x \in R$

Then, the solution of the given inequation is $\left(-\infty, \frac{5}{2}\right)$.

(ii) $x \in Z$

Then, the solution of the given inequation is $\{\ldots \ldots \ldots-3,-2,-1,0,1,2\}$.

(iii) $x \in N$

Then, the solution of the given inequation is $\{1,2\}$.