SOLUTION: If -4<-2t+6<10,then 2>t+6>-5 Is this true or false? If false,please correct the 2>t+6>-5 part. Thank you for taking time to help me.

Algebra ->  Inequalities -> SOLUTION: If -4<-2t+6<10,then 2>t+6>-5 Is this true or false? If false,please correct the 2>t+6>-5 part. Thank you for taking time to help me.      Log On


   

Question 1057768: If -4<-2t+6<10,then 2>t+6>-5 Is this true or false? If false,please correct the 2>t+6>-5 part.
Thank you for taking time to help me.
Answer by solve_for_x(190) About Me  (Show Source):
You can put this solution on YOUR website!
This is false.

Starting with the original compound inequality:

-4 < -2t + 6 < 10

Subtract 6 from each expression to get:

-4 - 6 < -2t + 6 - 6 < 10 - 6

-10 < -2t < 4

Dividing through by -2, and reversing the inequality signs, gives:

-10 / -2 > t > 4 / -2

5 > t > -2

Reversing this compound inequality gives:

-2 < t < 5

Adding 6 back to eat portion gives:

-2 + 6 < t + 6 < 5 + 6

4 < t + 6 < 11, which is not the same as 2 > t + 6 > 5