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Question 269050: Please help me solve this problem:
(x+2)(x-8)(x+1)>0
Use at least one inequality or compound inequality to express your answer. For answers with more than one inequality seperate the inequalities by a comma.
thanks.
Answer by persian52(161)   (Show Source):
You can put this solution on YOUR website! Here you go my friend, hope it helped!
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(x+2)(x-8)(x+1)>0
If any individual factor on the left-hand side of the equation is equal to 0, the entire expression will be equal to 0.
(x+2)=0_(x-8)=0_(x+1)=0
Set the first factor equal to 0 and solve.
(x+2)=0
Remove the parentheses around the expression x+2.
x+2=0
Since 2 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2 from both sides.
x=-2
Set the next factor equal to 0 and solve.
(x-8)=0
Remove the parentheses around the expression x-8.
x-8=0
Since -8 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 8 to both sides.
x=8
Set the next factor equal to 0 and solve.
(x+1)=0
Remove the parentheses around the expression x+1.
x+1=0
Since 1 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 1 from both sides.
x=-1
To find the solution set that makes the expression greater than 0, break the set into real number intervals based on the values found earlier.
x<-2_-2
Determine if the given interval makes each factor positive or negative. If the number of negative factors is odd, then the entire expression over this interval is negative. If the number of negative factors is even, then the entire expression over this interval is positive.
x<-2 makes the expression negative_-2
Since this is a 'greater than 0' inequality, all intervals that make the expression positive are part of the solution.
Answer: -28
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