Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 3 - Linear and Quadratic Functions - 3.5 Inequalities Involving Quadratic Functions - 3.5 Assess Your Understanding - Page 160: 15

Answer

$x$ is in the inverval: $(-0.5,3)$.

Work Step by Step

$2x^2<5x+3$ I subtract $(5x+3)$ from both sides: $2x^2-5x-3<0.$ The coefficient of $x^2$ is $2$, hence the coefficient of the xs in the multipliers should be $2$ and $1$. The coefficient of $x^0$ is -3, hence the coefficient of the $x^0$s in the multipliers should be $-3$ and $1$ or $3$ and $-1$. Hence the following combination is good: $(2x+1)(x-3)<0$. Therefore $x$ is in the inverval: $(-0.5,3)$ according to the graph.
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