Question

6x – 4 < –34 or 3x + 10 > 10

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 

 TO CHECK: 

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

Answer 2

Left side: x < -5

Right side: x > 0

Not sure if you want to graph it on a number line or a coordinate plane