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Chapter 7: Q.474. (page 741)

Solve the rational inequality and write the solution in interval notation.

5xx-2>1

Short Answer

Expert verified

The solution is x<-12orx>2.

In interval notation-鈭�,-12鈭�2,鈭�.

Step by step solution

01

Step 1. Given information.

The given rational inequality is5xx-2>1.

02

Step 2. Solve the given inequality.

5xx-2>15xx-2-1>05x-x+2x-2>04x+2x-2>022x+1x-2>0

03

Step 3. Find all the values where the expression switches from negative to positive by setting each factor equal to zero.

22x+1=02x+1=0x=-12or x-2=0x=2

The domain of the given inequality is -鈭�,2鈭�2,鈭�.

04

Step 4. Simplified answer.

The solution consists of all of the true intervals.

x<-12or x>2

The required solution in interval notation is-鈭�,-12鈭�2,鈭�.

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