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Question 1169706: Can you help me solve this inequality and graph the solution?
2k - 6 > 3k + 2
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 2k - 6 > 3k + 2 Put the k on the left
-k>8 divide by -1 and flip inequality
k <-8
This is on the number line with an open circle at -8 and the arrow going to the left.
Check this.
0 should not work and -6 is not > than 2
-10 should work and -26>-28
Answer by ikleyn(52814)  (Show Source):
You can put this solution on YOUR website! .
This inequality is for one single unknown "k", so its solution is some set of real numbers in number line.
First, subtract 2k from both sides. You will get an equivalent inequality
2k - 2k - 6 > 3k - 2k + 2
Combine like terms. You will get
-6 > k + 2.
Next, subtract 2 from both sides. You will get an equivalent inequality
-6 - 2 > k + 2 - 2.
Combine like terms. You will get
-8 > k.
It is the same as
k < -8.
At this point, the solution is completed.
The answer is k < -8.
It is the set of all real numbers that are less than -8.
These numbers (the solution set) are located at the number line on the left from the point k= -8.
The point k= -8 itself IS NOT INCLUDED to the solution set.
Graphically, the solution set is shown below
{ k < -8 }
===================)------------------------------------
-8
Or, in the interval notation, the solution set is (-oo,-8).
The symbol -oo represents "minus infinity".
The solution is completed.
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Is everything clear to you in it ?
If you have question, do not hesitate to post them to me.
To continue your education on this subject, see the lesson
- Solving simple and simplest linear inequalities
in this site.
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