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1. 1/3 +2/(1-x) >0

For x<1 , the inequality can be simplified as

1-x + 6 >0

x< 7

the solution is

x<1

for x>1, the inequality can be simplified as

1-x+6 <0

x>7

the solution is x>7

therefore, the set can be written as

{xR|x<1x>7}

2. For x<-1, the inequality can be simplified as

-x-1+2-2x>1

-3x >0

x<0

the solution is

x<-1

for -1x1, the inequality becomes

x+1+2-2x>1

-x >-2

x<2

The solution is

-1x1

for x>1, the inequality becomes

x+1+2x-2>1

3x>2

x>2/3

the solution is x>1

therefore, the set can be written as

{xR}

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1. 1/3 +2/(1-x) >0 For x0 x< 7 the solution is x1, the inequality can be simplified as 1-x+6 7 the solution is x>7 therefore, the set can be written as {xR|x7} 2. For x1 -3x >0 x-2 x1, the inequality becomes x+1+2x-2>1 3x>2 x>2/3 the solution is x>1 therefore, the set can be written as {xR} 3. A={xR|-1 ...
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