Question 1094222
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If you want to write "absolute value inequality", then do not use brackets [ ] instead of absolute value sign.


Use |7-5x| >= 15.


If it is what you want, then confirm please.




<U>comment from student</U>: Yes, this is what I was trying to write.



<U>My response</U>.  OK. So, I will explain you how to solve an inequality


|7-5x| >= 15



<pre>
Divide both sides by 5. You will get an equivalent inequality

|7/5 - x| >= 3.


Its solutions are those "x" that are remoted at least in 3 units from the point {{{7/5}}} on the number line.


So, the solution set is  x <= {{{7/5-3}}}  and  x >= {{{7/5+3}}},  or, which is the same,

x <= {{{-8/5}}}   and   x >=  {{{22/5}}}.


<U>Answer</U>.  The solution set is the union of two intervals [-infinity,-1.6] U [4.4,infinity]  on the number line.
</pre>

Solved.