Question

Can someone please help with solving compound inequality.
!.) 6x-4<-34 or 3x+10>10
2.) -2<=2x-4<4
I'd appreciate if someone can explain not looking for just answer. Thank you

Answer 1

1. 6x-4< -34, or 3x+10 > 10.

6x-4 < -34.
6x < -34 + 4
6x < -30
X < -5.

3x + 10 > 10.
3x > 10 - 10
3x > 0
X > 0.

2. -2 <= 2x-4 < 4.
Add 4 to each end and the center:
-2 + 4<= 2x-4+4 < 4+4.
2 <= 2x < 8
Divide each end and center by 2:
1 <= X < 4.

The compound inequality is actually 2
inequalities and can be solved separately:

2x-4 => -2, and 2x-4 < 4.

2x-4 => -2.
2x => -2+4
2x=> 2
X => 1.

2x-4 < 4.
2x < 4+4
2x < 8
X < 4.

Solution: 1< = X < 4. or X => 1, and X<4

CHECK:

1. Substitute any number < -5 for X.
Eq2: Subst. any number > 0 for X.

Answer 2

Thank you for showing me how to do these really helps alot.

Answer 3

u sure brandon, we needed a line to see