solve inequalities

[sandra23860]

3<2-x<=5

4+1/2(x)=2

 

[tkhunny]

3<2-x<=5

One piece at a time.

3 < 2-x
Add x
3+x < 2
Subtract 3
x < -1

2-x <= 5
Add x
2 <= 5+x
Subtract 5
-3 <= x

Intersection
-3 <= x < 1

Check

3<2-(-2)<=5 ??
3<2+2<=5 ??
3<4<=5 Looks good.

4+1/2(x)=2

Subtract 4
1/2(x)=-2
Multiply by 2
x = -4

Check

4+1/2(-4)=2 ??
4-2=2 ??
2 = 2 Looks good.

OK, now what was it you wanted? Where were you having trouble?