Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Solve the inequality algebraically
$(x - 1) (x - 2) (x - 3) \leq 0$

Required solution set is

$(- \infty, 1] \cup [2, 3]$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1.Given information

we have a given inequality

$(x - 1) (x - 2) (x - 3) \leq 0$

Step 2.Finding the zeros

Zeroes of inequality

$f (x) = (x - 1) (x - 2) (x - 3) \leq 0$

are,

$x = 1 x = 2 x = 3$

Step 3.Divide the real number line into 4 intervals

Now we use the zeros to separate the real number line into intervals.

$(- \infty, 1), (1, 2), (2, 3), (3, \infty)$

Step 4.Selecting a test number in each interval

Now we select a test number in each interval found in Step 3 and evaluate at each number to determine if $f (x) = (x - 1) (x - 2) (x - 3) = 0$

is positive or negative.

In the interval $(- \infty, 1)$ we chose 0, where f is negative

In the interval $(1, 2)$

we chose 1.5 , where f is positive.

In the interval (2,3) we chose 2.5 , where f is negative.

In the interval $(3, \infty)$

we chose 4 , where f is positive.

We know that our required inequality is $f (x) \leq 0$

Here the inequality is strict $(\geq o r \leq)$ so we have to include the solutions of $f (x) = 0$

in the solution set.

So we want the interval where f is negative or equals to 0.

So required solution set is $(- \infty, 1] \cup [2, 3]$

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Solve the inequality algebraically
$(x - 1) (x - 2) (x - 3) \leq 0$

Step by Step Solution

Step 1.Given information

Step 2.Finding the zeros

Step 3.Divide the real number line into 4 intervals

Step 4.Selecting a test number in each interval

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Solve the inequality algebraically(x-1)(x-2)(x-3)≤0

Step by Step Solution

Step 1.Given information

Step 2.Finding the zeros

Step 3.Divide the real number line into 4 intervals

Step 4.Selecting a test number in each interval

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Solve the inequality algebraically
$(x - 1) (x - 2) (x - 3) \leq 0$