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3 years ago

What is the solution to 4/a+5/3a<3

Mathematics

1 answer:

scoray [572]3 years ago

3 0

$\dfrac{4}{a}+\dfrac{5}{3a} < 3\ \ \ |-3\ \ \ assume\ a\neq0\\\\\dfrac{3\cdot4}{3a}+\dfrac{5}{3a}-\dfrac{3a\cdot3}{3a} < 0\\\\\dfrac{12+5-9a}{3a} < 0\\\\\dfrac{-9a+17}{3a} < 0\iff 3a(-9a+17) < 0\\\\3a=0\to a=0\\\\-9a+17=0\to a=\dfrac{17}{9}$
Look at the picture.
$Answer:\ a\in\left(0;\ \dfrac{17}{9}\right)$

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To find the value, first, we need to use the half-angle formula:

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Then,

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Then,

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Then,

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