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Question 1156720: 5x-19< or equal to 1 OR -4x+3<-6
What is the answer
X> or equal to 4
X> -9/4
There are no solutions
All values are solutions
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source):
Answer by ikleyn(52879)  (Show Source):
You can put this solution on YOUR website! .
This problem is of great educational value and of great educational importance.
The solution by the other tutor (in its final part) is INCORRECT,
so I came to bring the correct version.
You are given a system of inequalities
5x - 19 <= 1 OR -4x + 3 < -6.
It consists of two inequalities, connected by a service word " OR ".
It means that you should solve EACH inequality SEPARATELY, and then the solution to this SYSTEM of inequalities
is the UNION of the solution sets to each separate inequalities.
The first inequality and its solution are
5x - 19 <= 1 ===> 5x <= 1 + 19 ===> 5x <= 20 ===> x <= 20/5 ===> x <= 4.
The second inequality and its solution are
-4x + 3 < -6 ===> 3 + 6 < 4x ===> 9 < 4x ==== x >  .
So, the solution sets are x<= 4 for the first inequality and x > for the second inequality.
The solution set for the SYSTEM with the service word " OR " is the UNION of these two sets.
But, as it is OBVIOUS, the UNION covers the ENTIRE SET of ALL REAL numbers.
Therefore, the ANSWER to the problem's question is THIS :
the solution to the given system is the ENTIRE SET of ALL REAL numbers.
Solved.
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On this subject, see the lessons
- Solving systems of linear inequalities in one unknown
- Solving compound inequalities
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Inequalities".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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