SOLUTION: can you please help me solve the inequality in interval notation 2x-2< x+6< 3x-4 I tried moving everything to the left and got (-infinity,3) but that is incorrect

Algebra ->  Inequalities -> SOLUTION: can you please help me solve the inequality in interval notation 2x-2< x+6< 3x-4 I tried moving everything to the left and got (-infinity,3) but that is incorrect      Log On


   

Question 1093350: can you please help me solve the inequality in interval notation
2x-2< x+6< 3x-4
I tried moving everything to the left and got (-infinity,3) but that is incorrect
Found 2 solutions by josgarithmetic, Boreal:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
2x-2%3C+x%2B6%3C+3x-4

That means
system%282x-2%3Cx%2B6%2CAND%2Cx%2B6%3C3x-4%29

-

-
x-2%3C6
x%3C8
-

x%2B6%3C3x-4
6%3C2x-4
10%3C2x
5%3Cx
-
The way that BOTH x%3C8 AND x%3E5 is that these solutions of x are highlight%285%3Cx%3C8%29.

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
2x-2< x+6< 3x-4
work on the left two
x< 8
work on the right two
=-2x < -10
x > 5
(5, 8)
check
try 0, shouldn't work. -2<6<-4, doesn't work
try 9, shouldn't work. -20<-3<-31 doesn't work
try 6 should work 10 < 12 < 14
7 should 12 < 13 <17
5 and 8 are just outside
8 < 11 < 11
14 < 14 < 20