Solving the inequality 6 - 4x ≥ 2x - 3

[Gringo123]

6 - 4x (is more than or equal to) 2x - 3

The answer to this inequality is:
x is less than or equal to 1.5

I got this far before getting stuck:

add 3 to both sides:
9 - 4x (is more than or equal to) 2x

divide by 2:
4.5 - 2x (is more than or equal to) x

How do I finish this off?

 

[Fightfish]

You know, you can just shift terms across the inequality as though its an ordinary equal sign (similar arithmetic rules apply!)
So, try to make x the subject on one side, as though you are solving a simple equality equation!

 

[Dollydaggerxo]

6 - 4x >= 2x - 3
6 - 4x - 2x >= -3
- 6x >= -3 - 6
-6x >= -9
x <= -9/-6
x <= 1.5

 

[Gringo123]

Thanks a lot guys! Just 1 more question.
If x <= 1.5
is it correct to say:
-x >= -1.5
In other words, does the <= invert when the figures involved go from negative to positive?
Thanks again!

 

[Mark44]

The direction of the inequality changes when you multiply both sides by a negative number.