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Solve this inequality

  • Thread starter Gringo123
  • Start date
  • #1
141
0
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?
 

Answers and Replies

  • #2
954
117
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!
 
  • #3
6 - 4x >= 2x - 3
6 - 4x - 2x >= -3
- 6x >= -3 - 6
-6x >= -9
x <= -9/-6
x <= 1.5
 
  • #4
141
0
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!
 
  • #5
33,627
5,284
The direction of the inequality changes when you multiply both sides by a negative number.
 

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