Question

Mark the correct alternative in each of the following: 

If − 3x\[+\]17\[< -\]13, then

Options

• (a) x\[\in\](10, \[\infty\]

• (b) x\[\in\][10, \[\infty\]

• (c) x\[- \infty\]10]

• (d) x\[\in\]\[-\]10, 10) 

Answer 1

\[- 3x + 17 < - 13\]
\[\text{ Subtracting 17 on both sides, we get }\]
\[ \Rightarrow - 3x + 17 - 17 < - 13 - 17\]
\[ \Rightarrow - 3x < - 30\]
\[\text{ Dividing - 3 on both sides, we get }\]
\[ \Rightarrow \frac{- 3x}{- 3} > \frac{- 30}{- 3}\]
\[ \Rightarrow x > 10\]
\[ \Rightarrow x \in \left( 10, \infty \right)\]