anonymous
  • anonymous
Solve the inequality, (x+3)(x-2)>0. Express your answer using set notation.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Imagine x is a big negative number? What will the result of this expression be?
myininaya
  • myininaya
(x+3)(x-2) is 0 when x=-3 and 2. So use test points before and after -3 and 2 to see what are happening to the factors. so plug in some number before -3 like -4 so -4+3=-1 -4-2=-6 (-1)(-6)=6>0 so part of the solution is x is (-inf,-3) now plug in a number between -3 and 2 like 0 so 0+3=3 0-2=-2 (3)(-2)=-6<0 so the interval (-3,2) is not apart of the solution now you do the last interval
anonymous
  • anonymous
If x is a big negative numer x+3 will still be big and negative, and x-2 will also be negative. A negative times a negative is positive. So big negative values for x are ok.

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anonymous
  • anonymous
Now as x gets close to -3 from the negative infinity side, the (x+3) factor will start getting closer and closer to 0. Once x = -3 we see that the expression becomes 0, so this is not allowed.
anonymous
  • anonymous
So our first interval is \((-\infty,-3)\). Now if x is between -3 and 2 what will this expression be?
anonymous
  • anonymous
so the last interval would be, (2,inf)?
myininaya
  • myininaya
is that part of the solution? let's check: 3+3=6 3-1=2 6(2)>0 so yes thats right so your whole answer is (-inf,3)U(2,inf)
myininaya
  • myininaya
that 3 is suppose to be negative
myininaya
  • myininaya
(-inf,-3)U(2,inf)
anonymous
  • anonymous
is that part of the solution? let's check: 3+3=6 3-1=2*** 6(2)>0 so yes thats right so your whole answer is (-inf,3)U(2,in *** the 3-1, isnt it suppose to be 3-2?
myininaya
  • myininaya
yes but we still get something positive no biggie little type-0

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