help with solving inequalities please?

Question

2x > -6 and x - 4 < 3

x + 3 > 2x + 1 and -4x < -8

-6 < x + 3 < 6

-3x > -6 or x - 5 < 2

x - 2 > 2x + 1 or 10 > -2x + 2

Answer 1

2x > -6 and x - 4 < 3
x>-3 and x<7 --> -3
x + 3 > 2x + 1 and -4x < -8
2>x and x>2 --> x not = 2

-6 < x + 3 < 6
-9< x <3

-3x > -6 or x - 5 < 2
x>2 or x<7 --> 2
x - 2 > 2x + 1 or 10 > -2x + 2
3 > x or 4 > -x
3>x or 4 (-infinity,3) U (4, infinity)

Answer 2

(a) (2x >-6) = (x>-3) and (x-4<3)= (x<7)
then -3 (b) (x+3 > 2x+1) = (2 >x) and (-4x<-8) = (x>2)
then x = {} (means nothing)
(c) (-6 (d) (-3x>-6)=(x<2) or (x-5<2) = (x<7)
then x<7
(e) (x-2>2x+1) = (-3>x) or (10>-2x+2) = (4 then (x>4 or x<-3)

Answer 3

ps,i assume there are 5 questions and not 1 big qn.

1) 2x> -6 and x-4<3
for 2x>-6,
x>-3

for x-4<3
x<7

thus, to satisfy both inequalities, -3
2) x+3>2x+1 and -4x<-8
for x+3>2x+1
3-1>2x-x
so,x<2

for -4x<-8
4x>8(cos we "remove" the -ve sign so we have to switch the direction of the inequality sign)
so,x>2

thus,x<2 or x>2

3)-6 we break it into 2 parts,
a)-6 -9 x>-9

b)x+3<6
x<3

thus, -9
4) -3x>-6 or x-5<2
for -3x>-6
3x<6
x<2

for x-5<2
x<7

thus, x<7 or x<2

5)x-2>2x+1 or 10>-2x+2
for x-2>2x+1
-3>x
x<-3

for 10>-2x+2
8>-2x
-8<2x
-4
thus, -4