Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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X − 2 ≤ 5 X + 8 3 - Mathematics

\[x - 2 \leq \frac{5x + 8}{3}\] 

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Solution

\[x - 2 \leq \frac{5x + 8}{3}\]
\[ \Rightarrow 3\left( x - 2 \right) \leq 5x + 8 \left[ \text{ Multiplying both the sides by 3 } \right]\]
\[ \Rightarrow 3x - 6 \leq 5x + 8\]
\[ \Rightarrow 5x + 8 \geq 3x - 6\]
\[ \Rightarrow 5x - 3x \geq - 6 - 8 \left[ \text{ Transposing 3x to the LHS and 8 to the RHS } \right]\]
\[ \Rightarrow 2x \geq - 14\]
\[ \Rightarrow x \geq - 7 \left[ \text{ Dividing both the sides by 2 } \right]\]
\[\text{ Hence, the solution of the given inequation is } [ - 7, \infty ) .\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 15 Linear Inequations
Exercise 15.1 | Q 18 | Page 10
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