SOLUTION: For the following compound​ inequality, give the solution set in both interval and graph forms. x≥−5 or x≥6

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Question 1151645: For the following compound​ inequality, give the solution set in both interval and graph forms.
x≥−5 or x≥6
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

or
indicates all the numbers to the right of including , and indicates all the numbers to the right of including .
The intersection of these two graphs is all the numbers from - 5 to infinity.
The solution set is:
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Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.

The given system of inequalities is


    x >= -5  or  x >= 6.


Notice that the two inequalities are connected by the service word " or ".


It means that the solution to the system is THE UNION of the solutions to each partial inequality.


The solution for the inequality x >= -5  is the set  [-5,oo).

The solution for the inequality x >= 6 is the set [6,oo).


The UNION of these sets is the interval  [-5,oo), i.e. the set of all real number greater or equal to -5.    ANSWER


My answer is the same as in the post by @MathLover1.

But she made 2 fatal errors in her post.

First,  she write that the solution is the intersection of two partial subsets --- IT  IS  WRONG.

Second,  instead of taking intersection,  in her post she takes the union.

So,  after making two fatal errors,  she came to the correct answer.

It is why I came to warn you and to bring the correct solution.


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On solving systems of inequalities and compound inequalities, see the lessons
    - Solving systems of linear inequalities in one unknown
    - Solving compound inequalities
in this site.



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