Question

\[x - 2 \leq \frac{5x + 8}{3}\] 

Answer 1

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