Precalculus with Limits

3rd Edition

ISBN: 9781133947202

Author: Ron Larson

Publisher: Cengage Learning

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Question

Chapter 2.7, Problem 29E

To determine

ToSolve: The inequality $4x3−6x2<0$ and graph the solution set.

Expert Solution & Answer

Answer to Problem 29E

Thesolution set of the given inequality is $(−∞,0)∪(0,32)$

Graph of the solution set is

Precalculus with Limits, Chapter 2.7, Problem 29E , additional homework tip 1

Explanation of Solution

Given:

The inequality $4x3−6x2<0$

Concept Used:

Solving an inequality means, finding all the values of the variable for which inequality satisfy.

Calculation:

Given the inequality $4x3−6x2<0$

Consider

$4x3−6x2=0$

$4x3−6x2=02x2(2x−3)=0$

That is

$2x2=0$ and $2x−3=0$

$x=0$ and $x=32$

The key numbers are $x=0$ and $x=32$

The test intervals are $(−∞,0)$ , $(0,32)$ and $(32,∞)$

Evaluating the left side of the inequality (polynomial value) for a $x−value$ in each test interval.

Test Interval	$x−value$	Polynomial Value	Conclusion
$(−∞,0)$	$x=−1$	$4x3−6x2=4(−1)3−6(−1)2 =−4−6=−10$	Negative
$(0,32)$	$x=1$	$4x3−6x2=4(1)3−6(1)2 =4−6=−2$	Negative
$(32,∞)$	$x=3$	$4x3−6x2=4(3)3−6(3)2 =108−54=54$	Positive

The inequality is satisfied for all the $x−values$ in the interval $(−∞,0)$ and $(0,32)$ .

Therefore, the solution set of the given inequality is $(−∞,0)∪(0,32)$

Plotting all the points of the solutions set on the graph, we have:

Precalculus with Limits, Chapter 2.7, Problem 29E , additional homework tip 2

Conclusion:

Thesolution set of the given inequality is $(−∞,0)∪(0,32)$

Graph of the solution set is

Precalculus with Limits, Chapter 2.7, Problem 29E , additional homework tip 3

Chapter 2.7, Problem 28E

Chapter 2.7, Problem 30E

Chapter 2 Solutions

Precalculus with Limits

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Prob. 3RE Ch. 2 - Prob. 4RE Ch. 2 - Prob. 5RE Ch. 2 - Prob. 6RE Ch. 2 - Prob. 7RE Ch. 2 - Prob. 8RE Ch. 2 - Prob. 9RE Ch. 2 - Prob. 10RE Ch. 2 - Prob. 11RE Ch. 2 - Prob. 12RE Ch. 2 - Prob. 13RE Ch. 2 - Prob. 14RE Ch. 2 - Prob. 15RE Ch. 2 - Prob. 16RE Ch. 2 - Prob. 17RE Ch. 2 - Prob. 18RE Ch. 2 - Prob. 19RE Ch. 2 - Prob. 20RE Ch. 2 - Prob. 21RE Ch. 2 - Prob. 22RE Ch. 2 - Prob. 23RE Ch. 2 - Prob. 24RE Ch. 2 - Prob. 25RE Ch. 2 - Prob. 26RE Ch. 2 - Prob. 27RE Ch. 2 - Prob. 28RE Ch. 2 - Prob. 29RE Ch. 2 - Prob. 30RE Ch. 2 - Prob. 31RE Ch. 2 - Prob. 32RE Ch. 2 - Prob. 33RE Ch. 2 - Prob. 34RE Ch. 2 - Prob. 35RE Ch. 2 - Prob. 36RE Ch. 2 - Prob. 37RE Ch. 2 - Prob. 38RE Ch. 2 - Prob. 39RE Ch. 2 - Prob. 40RE Ch. 2 - Prob. 41RE Ch. 2 - Prob. 42RE Ch. 2 - Prob. 43RE Ch. 2 - Prob. 44RE Ch. 2 - Prob. 45RE Ch. 2 - Prob. 46RE Ch. 2 - Prob. 47RE Ch. 2 - Prob. 48RE Ch. 2 - Prob. 49RE Ch. 2 - Prob. 50RE Ch. 2 - Prob. 51RE Ch. 2 - Prob. 52RE Ch. 2 - Prob. 53RE Ch. 2 - Prob. 54RE Ch. 2 - Prob. 55RE Ch. 2 - Prob. 56RE Ch. 2 - Prob. 57RE Ch. 2 - Prob. 58RE Ch. 2 - Prob. 59RE Ch. 2 - Prob. 60RE Ch. 2 - Prob. 61RE Ch. 2 - Prob. 62RE Ch. 2 - Prob. 63RE Ch. 2 - Prob. 64RE Ch. 2 - Prob. 65RE Ch. 2 - Prob. 66RE Ch. 2 - Prob. 1CT Ch. 2 - Prob. 2CT Ch. 2 - Prob. 3CT Ch. 2 - Prob. 4CT Ch. 2 - Prob. 5CT Ch. 2 - Prob. 6CT Ch. 2 - Prob. 7CT Ch. 2 - Prob. 8CT Ch. 2 - Prob. 9CT Ch. 2 - Prob. 10CT Ch. 2 - Prob. 11CT Ch. 2 - Prob. 12CT Ch. 2 - Prob. 13CT Ch. 2 - Prob. 14CT Ch. 2 - Prob. 15CT Ch. 2 - Prob. 16CT Ch. 2 - Prob. 17CT Ch. 2 - Prob. 18CT Ch. 2 - Prob. 1PS Ch. 2 - Prob. 2PS Ch. 2 - Prob. 3PS Ch. 2 - Prob. 4PS Ch. 2 - Prob. 5PS Ch. 2 - Prob. 6PS Ch. 2 - Prob. 7PS Ch. 2 - Prob. 8PS Ch. 2 - Prob. 9PS Ch. 2 - Prob. 10PS Ch. 2 - Prob. 11PS Ch. 2 - Prob. 12PS Ch. 2 - Prob. 13PS

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ToSolve: The inequality 4 x 3 − 6 x 2 &lt; 0 and graph the solution set.

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ToSolve: The inequality 4x3−6x2<0<m:math><m:mrow><m:mn>4</m:mn><m:msup><m:mi>x</m:mi><m:mn>3</m:mn></m:msup><m:mo>−</m:mo><m:mn>6</m:mn><m:msup><m:mi>x</m:mi><m:mn>2</m:mn></m:msup><m:mo>&lt;</m:mo><m:mn>0</m:mn></m:mrow></m:math> and graph the solution set.

Answer to Problem 29E

Explanation of Solution

Chapter 2 Solutions

ToSolve: The inequality 4 x 3 − 6 x 2 < 0 and graph the solution set.

ToSolve: The inequality $4x3−6x2<0$ and graph the solution set.