Question 1156720
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            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.



<pre>
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 <U>UNION</U> 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 > {{{9/4}}}.


So, the solution sets are  x<= 4 for the first inequality and  x > {{{9/4}}} 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 <U>ANSWER</U> to the problem's question is THIS :

    the solution to the given system is the ENTIRE SET of ALL REAL numbers.
</pre>

Solved.


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On this subject, see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Inequalities/Solving-systems-of-linear-inequalities-in-one-unknown.lesson>Solving systems of linear inequalities in one unknown</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Inequalities/Solving-compound-inequalities.lesson>Solving compound inequalities</A> 

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic &nbsp;"<U>Inequalities</U>".



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.