Question 1137380
.
<pre>
This problem wants you solve two inequalities separately

    x + 2 < 5      (1)
and
    x - 7 > -6     (2)

and then take the intersection of their sets of solutions.



It is the same as to solve the system of two inequalities 

{{{system(x+2 < 5,

          x -7 > -6
)}}}


OK. So, our first step is to solve inequality (1).  For it, subtract the number 2 from both sides. 
Inequality remains equivalent and takes the form

    x < 5 - 2,  
 
which is the same as

    x < 3.


So, the set of solutions to the first inequality is  { x < 3 }, or, in the interval notation  ({{{-infinity}}},{{{3}}}).


Our next step is to solve inequality (2).  For it, add the number 7 to both sides. 
Inequality remains equivalent and takes the form

    x > -6 + 7,  
 
which is the same as

    x > 1.


Thus the set of solutions to this inequality is  { x > 1 }, or, in the interval notation  ({{{1}}},{{{infinity}}}).


The intersection of the sets  { x < 3 }  and  { x > 1} is the set  { 1 < x < 3 },  or, in the interval notation,  interval (1,3).


<U>ANSWER</U>.  The solution of the problem is the set  { 1 < x < 3 },  or, in the interval notation,  interval (1,3).
</pre>

Solved.


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


To find other similar solved problems, see the lesson 

&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.