SOLUTION: question 4x-9/10<=-9 or 4x-9/10>=6 {x|x<=? or x>=?} question Graph the inequality on a plane Y>5x Thank you

Algebra ->  Inequalities -> SOLUTION: question 4x-9/10<=-9 or 4x-9/10>=6 {x|x<=? or x>=?} question Graph the inequality on a plane Y>5x Thank you      Log On


   

Question 168710: question 4x-9/10<=-9 or 4x-9/10>=6 {x|x<=? or x>=?}
question Graph the inequality on a plane Y>5x
Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Question 1: Is the term "10" underneath every term or just 1? In other words, is the first inequality %284x-9%29%2F10%3C=-9 or is it 4x-9%2F10%3C=-9 ???


Question 2:

Graph the inequality on a plane Y>5x



In order to graph y%3E5x, we need to graph the equation y=5x (just replace the inequality sign with an equal sign).
So lets graph the line y=5x (note: if you need help with graphing, check out this solver)


+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+5x%29+ graph of y=5x


Now lets pick a test point, say (0,1). Any point will work, (just make sure the point doesn't lie on the line). Now evaluate the inequality y%3E5x with the test point

Substitute (0,1) into the inequality


1%3E5%280%29 Plug in x=0 and y=1


1%3E0 Multiply


Since this inequality is true, we simply shade the entire region that contains (0,1). This means that we shade the ENTIRE region that is above the line (since the point (0,1) lies in the region above the line)


Graph of y%3E5x with the shaded region in green


Note: the line should be a dotted/dashed line