SOLUTION: Solve and give answer in interval notation {{{x^2 >= 3*x+4}}}

Algebra ->  Graphs -> SOLUTION: Solve and give answer in interval notation {{{x^2 >= 3*x+4}}}      Log On


   

Question 135439: Solve and give answer in interval notation

x%5E2+%3E=+3%2Ax%2B4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given inequality


Move all terms to the left side


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+-1%2C4+%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=-2

Start with the given inequality

Plug in x=-2

Evaluate and simplify



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


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


Start with the given inequality

Plug in x=0

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.
-----------------------------------------------


So let's evaluate a point that is to the right of (which is the right most endpoint). Let's evaluate the value x=5

Start with the given inequality

Plug in x=5

Evaluate and simplify



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


Answer:


So the answer in interval notation is


(][)