SOLUTION: Solve and give answer in interval notation {{{(x+5)(3x-4)>0}}}

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Question 135369: Solve and give answer in interval notation

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Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given inequality


Set the left side equal to zero

Solve for x in each case

So this means that the critical values are




Now plot the critical values on a number line

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So let's evaluate a point that is to the left of (which is the left most endpoint). Let's evaluate the value x=-6

Start with the given inequality

Plug in x=-6

Evaluate and simplify



Since is true, this means that everything to the left of x=-6 is in the solution set. So the graph looks like this



So one part of the solution in interval notation is
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Now let's test a point that is in between the critical values and


Start with the given inequality

Plug in x=-2

Evaluate and simplify


Since is false, this means that the interval does not work. So that means that this interval is not in the solution set and can be ignored.
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So let's evaluate a point that is to the right of (which is the right most endpoint). Let's evaluate the value x=2

Start with the given inequality

Plug in x=2

Evaluate and simplify


So everything to the right of is in the solution set. So our graph now looks like



Since is true, this means that one part of the solution in interval notation is
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Answer:

So the solution in interval notation is