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andre [41]
3 years ago
9

Solve the inequality

Formula1" title=" \frac{2x}{x + 3} \leqslant 3" alt=" \frac{2x}{x + 3} \leqslant 3" align="absmiddle" class="latex-formula">
The solution set is

Mathematics
1 answer:
Fofino [41]3 years ago
3 0

Domain:x\neq-3\\\\\dfrac{2x}{x+3}\leq3\qquad\text{subtract 3 from both sides}\\\\\dfrac{2x}{x+3}-3\leq0\\\\\dfrac{2x}{x+3}-\dfrac{3(x+3)}{x+3}\leq0\\\\\dfrac{2x}{x+3}-\dfrac{3x+9}{x+3}\leq0\\\\\dfrac{2x-(3x+9)}{x+3}\leq0\\\\\dfrac{2x-3x-9}{x+3}\leq0\\\\\dfrac{-x-9}{x+3}\leq0\Rightarrow(x+3)(-x-9)\leq0\\\\x=-3,\ x=-9\\\\x\in(-\infty,\ -9]\ \cup\ (-3,\ \infty)

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