SOLUTION: For the following compound​ inequality, give the solution set in both interval and graph form. x+2>7 or −4x+1≥9

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Question 1151646: For the following compound​ inequality, give the solution set in both interval and graph form.
x+2>7 or −4x+1≥9
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

or







solutions:
or
Interval notation:
(, ] or (,)

as you can see, indicates all the numbers to the left of (including ), and indicates all the numbers to the right of . The of these graphs contains . That is, the solution set is the . ∅
graph:
MSP5.gif


Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.

            The solution by @MathLover is   TOTALLY  WRONG.

            It is why I came to bring the correct solution. 


You are given the compound inequality, which is the system of two inequalities


    x+2 > 7  or  -4x+1 >= 9.


Notice that the inequalities are connected by the service word " or ", which means that the solution 

to the system is THE UNION of the solution sets for each individual inequality.



First inequality  x+2 > 7 has the solution x > 7, or, in the interval form  (7,oo).


Second inequality  -4x+1 >= 9  has the solution x <= -2, or, in the interval form (-oo,-2].



The solution to the given system of inequalities is THE UNION of these two intervals  (-oo,-2] U (7,oo).    ANSWER

Solved.

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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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