Algebra Honors II Combined Inequality Question!?

Question

i have this inequality question in my algebra book that i thought i knew how to do, but i checked my answer and it was wrong.

Heres the question....

2<(y+6)/2<5 and (4-y>5 or 4+y>7)

^^where i put the (y+6)/2... in the book it looks like y+6 over 2... with the fraction bar.

anyways the answer i got for this was

-4<y<-1 or y>3

which, when i checked in the book was wrong, the answer in the book was...

-2<y<-1 or 3<y<4

can someone explain how i got this wrong. and

how do get the answer in the book

everything i did looked like it was right.

Answer 1

the answer is who really cares

Answer 2

Not sure how you managed that!

If you look at part 1 of the 1st inequality only

2&lt;(y+6)/2   so   4&lt;y+6  so y&gt;-2

Part 2 is (y+6)/2&lt;5 so y+6&lt;10 so y&lt;4

Overall this means-2&lt;y&lt;4.

Now look at 1st part of 2nd inequality

4-y&gt;5 so y&lt;-1 and now for 2nd part

4+y&gt;7 so y&gt;3

Put them all together &amp; you have your answer.

Answer 3

1.  multiply both sides by 2

4 &lt; y + 6 &lt; 10

2.  subtract both sides by 6

-2 &lt; y &lt; 4

3.  using the next equations...you see that y must be smaller than -1 [ 4 - (-1) = 5...must be smaller than -1]

also y must be greater than 3 [ 4 + (3) = 7...must be bigger] so to satisfy all equations for y...

-2 &lt; y &lt; -1  and 3 &lt; y &lt; 4

-2 and 4 you get from solving the first equation

-1 from solving the 3rd equation

and 3 from solving the 4th equation

Answer 4

i think u makes a right one...

the answer on that book was wrong...