Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

In Problems 7–22, solve each inequality.
$4 x^{2} + 9 < 6 x$

The given inequality has no solution.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information

The given inequality is $4 x^{2} + 9 < 6 x$ .

Step 2. Find the Intercepts

Rewrite the inequality in standard form.

$4 x^{2} + 9 - 6 x < 0$

There are no real roots of $4 x^{2} + 9 - 6 x = 0$ , so, there are no x-intercepts of the curve.
The value of $f (0) = 9$ .
So, the y-intercept is $(0, 9)$ .
Find $x = \frac{- b}{2 a}$ to find the x - intercept of the vertex of parabola.

$x = \frac{6}{8}$

The value of $f (\frac{6}{8}) = \frac{27}{4}$ .
So, the vertex is $(\frac{6}{8}, \frac{27}{4})$ .

Step 3. Plot the Graph

Plot the parabola on a graph using the vertex and intercepts calculated in the previous step.

Step 4. Find the region below x-axis

From the graph, there is no region that lies below the x-axis.
So, the given inequality has no solution.

x	$y = f (x)$
-2	-26
-1	-4
0	2
1	-2
2	-10

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 7–22, solve each inequality.
$4 x^{2} + 9 < 6 x$

Step by Step Solution

Step 1. Given Information

Step 2. Find the Intercepts

Step 3. Plot the Graph

Step 4. Find the region below x-axis

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 7–22, solve each inequality.4x2+9<6x

Step by Step Solution

Step 1. Given Information

Step 2. Find the Intercepts

Step 3. Plot the Graph

Step 4. Find the region below x-axis

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In Problems 7–22, solve each inequality.
$4 x^{2} + 9 < 6 x$