SOLUTION: Solve the inequality -2(3 + x) < 4x + 4 < 8x. Give the result in set notation and graph it. My answer is {x|x >1} The graph looks like this __________(___________ _

Algebra ->  Inequalities -> SOLUTION: Solve the inequality -2(3 + x) < 4x + 4 < 8x. Give the result in set notation and graph it. My answer is {x|x >1} The graph looks like this __________(___________ _       Log On


   

Question 604725: Solve the inequality -2(3 + x) < 4x + 4 < 8x. Give the result in set notation and graph it.
My answer is {x|x >1}
The graph looks like this __________(_____________
1
I can't get to draw the arrow and the dark part of the line, but the dark part starts at the middle all the way down to the end.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Your answer is correct.

When you have A < B < C

You have to solve all three inequalities

     A < B,     B < C,    and A < C

and take as the final answer whatever result 
makes all three true at the same time. 

           -2(3 + x) < 4x + 4 < 8x

We do the first and second:

           -2(3 + x) < 4x + 4
             -6 - 2x < 4x + 4
                 -6x < 10
                   x > %28-10%29%2F6
                   x > -5%2F3
                 
We do the second and third:       

              4x + 4 < 8x
                  4x < 8x - 4
                 -4x < -4
                   x > 1 

We do the first and third:

           -2(3 + x) < 8x
             -6 - 2x < 8x
                -10x < 6
                   x > -6/10
                   x > -3/5

All three of these must be true at the same
time, so therefore x must be greater than 1

So the solution set is

          {x|x > 1}

Graphed on a number line:

 -------------------(============> 
 -5 -4 -3 -2 -1  0  1  2  3  4  5 

Edwin