SOLUTION: I am having trouble with solving inequalities. Can you please help? Solve the inequality: x^2-8x≤4x-36 If you could help I will greatly apprecaite it. Thanks in ad

Algebra ->  Inequalities -> SOLUTION: I am having trouble with solving inequalities. Can you please help? Solve the inequality: x^2-8x≤4x-36 If you could help I will greatly apprecaite it. Thanks in ad      Log On


   

Question 52872: I am having trouble with solving inequalities. Can you please help?
Solve the inequality: x^2-8x≤4x-36
If you could help I will greatly apprecaite it.
Thanks in advance.
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Set the problem <=0
x%5E2-8x%3C=4x-36
x%5E2-8x-4x%2B36%3C=4x-4x-36%2B36
x%5E2-12x%2B36%3C=0
Solve as if it's an equality, factor and solve for x:
%28x-6%29%28x-6%29=0
x-6+6=0+6
x=6
Since this is an inequality, we have to check values bigger and smaller than 6 to see what kind of inequality sign that we need.
When x=0,
(0-6)(0-6)=36, which is not less than 0.
When x=7
(7-6)(7-6)=1*1=1, which is also not less than 0.
Therefore, the only value for which
x%5E2-8x%3C=4x-36
is x=6
Interval notation:[6]
Set notation:{6}
Set Builder Notation:{x|x=6}