Need help with this
0<6-2x<4
x is greater than one and less than 3
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
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
To solve the inequality 0 < 6-2x < 4, we need to isolate x by performing the same operation on all three parts of the inequality.
1. Start by subtracting 6 from all three parts:
0 - 6 < 6 - 6 - 2x < 4 - 6
-6 < -2x < -2
2. Next, divide all three parts by -2. When dividing or multiplying by a negative number, remember to flip the inequality signs:
(-6)/(-2) > x > (-2)/(-2)
3 > x > 1
Therefore, the solution to the inequality 0 < 6-2x < 4 is 1 < x < 3.