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

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


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

x%2B2%3E7 or -4x%2B1%3E=9
x%2B2%3E7
x%3E7-2
x%3E5
-4x%2B1%3E=9
-9%2B1%3E=4x
4x%3C=-8
x%3C=-2
solutions:
x%3C=-2 or x%3E5
Interval notation:
(-infinity, -2] or (5,+infinity)

as you can see, x+%3C=-2 indicates all the numbers to the left of -2+(including -2), and x+%3E+5 indicates all the numbers to the right of 5. The intersection of these graphs contains no+numbers. That is, the solution set is the empty+set. ∅
graph:
MSP5.gif


Answer by ikleyn(52824) About Me  (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.

-----------------

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.