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