SOLUTION: Solve and give answer in interval notation {{{x^2-8x+12<=0}}}

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Question 135438: Solve and give answer in interval notation

x%5E2-8x%2B12%3C=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given inequality


Factor the left side


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

number_line%28+600%2C+-10%2C+10%2C+2%2C6+%29



So let's evaluate a point that is to the left of (which is the left most endpoint). Let's evaluate the value x=1

Start with the given inequality

Plug in x=1

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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Now let's test a point that is in between the critical values and


Start with the given inequality

Plug in x=4

Evaluate and simplify

So the graph now looks like





Since is true, this means that one part of the solution in interval notation is []




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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=7

Start with the given inequality

Plug in x=7

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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Answer:

So the solution in interval notation is
[]