SOLUTION: 2<3-1/2x<6

Algebra ->  Inequalities -> SOLUTION: 2<3-1/2x<6      Log On


   

Question 177247: 2<3-1/2x<6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%3C3-%281%2F2%29x%3C6 Start with the given compound inequality.


2-3%3C-%281%2F2%29x%3C6-3 Subtract 3 from ALL sides.


-1%3C-%281%2F2%29x%3C3 Combine like terms.


-1%28-2%29%3Ex%3E3%28-2%29 Multiply ALL sides by -2. Note: multiplying all sides of an inequality by a negative number will flip the signs.


2%3Ex%3E-6 Multiply


-6%3Cx%3C2 Rearrange the inequality


============================================

Answer:

So the solution is -6%3Cx%3C2



So the answer in interval notation is ()


Also, the answer in set-builder notation is


Here's the graph of the solution set on the number line:

Graph of the solution set

Note:
There is an open circle at x=-6 which means that we're excluding this value from the solution set
Also, there is an open circle at x=2 which means that we're excluding this value from the solution set.