Question

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

• A. $x\in \{-1,0,1,2,\dots \}$, 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, $3x+8>2$
Adding $-8$ on both sides,
$3x+8-8>2-8$
$\Rightarrow 3x>-6$
Dividing by 3 on both sides,
$\Rightarrow \frac{3x}{3}>\frac{-6}{3}$
$\Rightarrow x>-2$
(i) When $x$ is an integer, the solution of the given inequality is $\{-1,0,1,2\dots \}$.
(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.