Question

If $3 x+8>2$, then which of the following is true?

• A. $x \in\{-1,0,1,2, \ldots\}$, when $x$ is an integer
• B. $x \in[-2, \infty)$, when $x$ is a real number
• C. Both(a) and (b)
• D. None of the above

Answer 1

Answer: (A)

We have, $3 x+8>2$
Adding $-8$ on both sides,
$3 x+8-8 >2-8$
$\Rightarrow 3 x >-6$
Dividing by 3 on both sides,
$\Rightarrow \frac{3 x}{3}>\frac{-6}{3} $
$\Rightarrow x>-2$
(i) When $x$ is an integer, the solution of the given inequality is $\{-1,0,1,2 \ldots\}$.
(ii) When $x$ is a real number, the solution of the given inequality is $(-2, \infty)$. i.e., all the numbers lying between $-2$ and $\infty$ but $-2$ and $\infty$ are not included.