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Chapter 4: Q. 42 (page 246)

Solve each inequality. Graph the solution set.

6x+3鈮�1

Short Answer

Expert verified

The real zeroes are 3 and -3and the solution set can be graphed as

Step by step solution

01

Step 1. Given Information

The given inequality is6x+3鈮�1

02

Step 2. Calculation

Solve the given inequality as follows,

6x+3-1鈮�1-16x+3-1鈮�06x+3-1(x+3x+3)鈮�0-x+3x+3鈮�0

Now, let f(x)=-x+3x+3. We will find the real zeroes of the numerator and denominator.

-x+3=0鈬�x=3x+3=0鈬�x=-3

Thus, real zeroes of the function are-3and3

03

Step 3. Graph 

Construct the table by using a number from each interval to check whether the function is positive or negative.

Thus, the solution set is x|-3<x鈮�3

And the solution set can be graphed as

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(x-1)(x+1)x鈮�0
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