Need help with this

Question

0<6-2x<4

Answer 1

x is greater than one and less than 3

Answer 2

You have two inequalities:

1.

0 < 6 - 2 x

2.

6 - 2 x < 4

First inequalitie:

0 < 6 - 2 x

Add 2 x to both sides

0 + 2 x < 6 - 2 x + 2 x

2 x < 6

Divide both sides by 2

x < 3

Second inequalitie:

6 - 2 x < 4

Add 2 x to both sides

6 - 2 x + 2 x < 4 + 2 x

6 < 4 + 2 x

Subtract 4 to both sides

6 - 4 < 4 + 2 x - 4

2 < 2 x

Divide both sides by 2

1 < x

Merge overlapping intervals:

1 < x < 3

This mean:

x greater of 1 and less of 3

Answer 3

0<6-2x<4.
Subtract 6 from all 3 sides:
-6<-2x<-2,
Divide all 3 sides by -2 and reverse the inequality signs:
3>X>1.
This a compound inequality and is read as follows:
X is less than 3 and greater than 1.
Therefore, X lies between 1 and 3.

s