SOLUTION: How do you graph x + 5 > 2x + 1 and -4x < -8?

Algebra ->  Graphs -> SOLUTION: How do you graph x + 5 > 2x + 1 and -4x < -8?       Log On


   

Question 151736: How do you graph x + 5 > 2x + 1 and -4x < -8?

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

Let's solve the first inequality x%2B5%3E2x%2B1:


x%2B5%3E2x%2B1 Start with the first inequality.


x%3E2x%2B1-5 Subtract 5 from both sides.


x-2x%3E1-5 Subtract 2x from both sides.


-x%3E1-5 Combine like terms on the left side.


-x%3E-4 Combine like terms on the right side.


x%3C%28-4%29%2F%28-1%29 Divide both sides by -1 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3C4 Reduce.


---------------------------------------------------------------------


Now let's solve the second inequality -4x%3C-8:


-4x%3C-8 Start with the second inequality.


x%3E%28-8%29%2F%28-4%29 Divide both sides by -4 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3E2 Reduce.


So our answer is x%3C4 and x%3E2


This answer combines to the compound inequality 2%3Cx%3C4



So the answer in interval notation is ()


So the answer in set-builder notation is


Here's the graph of the solution set

Graph of the solution set

Note:
There is an open circle at x=2 which means that we're excluding this value from the solution set
Also, there is an open circle at x=4 which means that we're excluding this value from the solution set.