Solve the inequality. (Enter your answer using interval notation.) 2x^3 − 18x < x^2 − 9

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asked Dec 25, 2024 9.2k views

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Solve the inequality. (Enter your answer using interval notation.)
2x^3 − 18x < x^2 − 9

Mathematics
college

Matvore asked

by Matvore

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Answer:

Hi,

Explanation:

$2x^3-18x < x^2-9\\\\2x^3-x^2-18x+9 < 0\\\\x^2(2x-1)-9(2x-1) < 0\\\\(2x-1)(x^2-9) < 0\\\\(2x-1)(x+3)(x-3) < 0\\$

$\begin{array}cccccccx&&-3&&-(1)/(2) &&3&\\---&---&---&---&---&---&---&---\\2x-1&-&-&-&0&+&+&+\\x-3&-&0&+&+&+&+&+\\x+3&-&-&-&-&-&0&+\\---&---&---&---&---&---&---&---\\f(x)&-&0&+&0&-&0&+\\\end {array}\\\\\\x\in ]-\infty, -3[\ \cup\ ](1)/(2) , 3 [$

Len Greski answered Dec 29, 2024

by Len Greski

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Solve the inequality. (Enter your answer using interval notation.) 2x^3 − 18x < x^2 − 9

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