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Chapter 4: Q. 43 (page 246)

Solve each inequality. Graph the solution set.

2x-61-x<2

Short Answer

Expert verified

The real zeroes are 1 and 2 and the solution set can be graphed as

Step by step solution

01

Step 1. Given Information 

The given inequality is2x-61-x<2

02

Step 2. Calculation

Solve the given inequality as follows,

2x-61-x-2<2-22x-61-x-2<02x-61-x-2(1-x1-x)<04x-81-x<0

Now, let f(x)=4x-81-x. We will find the real zeroes of the numerator and denominator.

4x-8=0鈬�x=21-x=0鈬�x=1

Thus, real zeroes of the function are 1 and 2

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|x<-1orx>2

And the solution set can be graphed as

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