Solve the compound inequality-2<2x-4<4 answers are 0<x<-2,, 1<x<4, 1<x<0,, 3<x<6
just do the steps normally taken to solve equations
-2 < 2x-4 < 4
add 4 throughout to get
2 < 2x < 8
now divide by 2 to get
1 < x < 4
To solve the compound inequality -2 < 2x - 4 < 4, we need to isolate the variable x.
First, let's solve the left inequality: -2 < 2x - 4.
Add 4 to both sides: -2 + 4 < 2x - 4 + 4.
This simplifies to: 2 < 2x.
Next, let's solve the right inequality: 2x - 4 < 4.
Add 4 to both sides: 2x - 4 + 4 < 4 + 4.
This simplifies to: 2x < 8.
Now, let's solve each inequality separately:
1) 2 < 2x:
Divide both sides by 2: 2/2 < 2x/2.
This simplifies to: 1 < x.
2) 2x < 8:
Divide both sides by 2: 2x/2 < 8/2.
This simplifies to: x < 4.
So, we have x > 1 and x < 4 as our results. However, we need to find the intersection between these ranges since this is a compound inequality.
The intersection is where both inequalities are satisfied. In this case, it means finding where x is greater than 1 and less than 4. Therefore, our final solution is 1 < x < 4.