Question

solve 5-2x/3_< x/6 -5​

Answer 1

ANSWER:

To Solve:

• 5 - 2x/3 ≤ x/6 - 5

Solution:

$\text{We are given that,}\\\\:\longrightarrow5-\dfrac{2x}{3}\leqslant\dfrac{x}{6}-5\\\\\text{Taking LCM on both sides,}\\\\:\implies\dfrac{5(3)-2x}{3\!\!\!/}\leqslant\dfrac{x-30}{6\!\!\!/^{\:2}}\\\\:\implies15-2x\leqslant\dfrac{x-30}{2}\\\\\text{On cross-multiplying,}\\\\:\implies2(15-2x)\leqslant x-30\\\\:\implies30-4x\leqslant x-30\\\\\text{Bringing like terms together,}\\\\:\implies30+30\leqslant x+4x\\\\:\implies60\leqslant5x\\\\:\implies5x\geqslant60\\\\\text{Transposing 5 to RHS,}\\\\:\implies x\geqslant\dfrac{60\!\!\!\!/^{\:12}}{5\!\!\!/}\\\\\bf{:\implies x\geqslant12}$