Solve each open sentence?

Question

solve each open sentence
1) lx+2l>3
2) l2x-5l<_7
3) lx-1l _>4 and lxl _> 3

Answer 1

1) Set it up like this:
x+2<-3 or x+2>3 solve each one for x.
x<-5 or x>1

2) Set it up like this:
-7_<2x-5_<7 Add 5
-2_<2x_<12 Divide by 2
-1_
3) This one is just a bit tougher. Set up each
absolute value:
x-1_<-4 or x-1_>4 and x_<-3 or x_>3
x_<-3 or x_>5 and x_<-3 or x_>3
It has to be true for both since the word "and" is being used. For both inequalities it's true that x_<-3, but for _> they're different. x_>5 and x_>3 must be true for both so it has to be x_>5. The final answer: x_<-3 and x_>5.

Answer 2

1)
x + 2 > 3
x > 3 - 2
x > 1
or
x + 2 > -3
x > -3 -2
x > -5
So,
Solution = {x belongs to R | x >-5 or x > 1}
2)
l2x-5l<_7
2x <_7 + 5
2x <_12
x <_12/2
x<_6
or
2x - 5 <_-7
2x <_-7 + 5
2x <_ -2
x <_ -2/2
x <_ -1
Solution = {x belongs to R | x <_ -1 or x<_6}
3)
x - 1 _>4
x _> 4 + 1
x_> 5
or
x_> -4 + 1
x_> -3
Solution = {x belongs to R | x _> -3 or x_>5}
and
x_> 3 or x_> -3
::--::

Answer 3

1. X>3-2 or -X-2>3
1
2. 2X<_7+5 or -2x+5<_7
-1<_X<_6