Question 1209112
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Please help me with this:
5x-7 < 2x+5
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<pre>
They want you solve this inequality 

    5x - 7 < 2x + 5.


Apply a standard procedure solving linear inequality.


Add 7 to both sides of the inequality.  You will get an equivalent inequality

    5x - 7 + 7 < 2x + 5 + 7.


Combine like terms in both sides

    5x < 2x + 12.


Now subtract 2x from both sides.  You will get an equivalent inequality

    5x - 2x < 2x + 12 - 2x.


Combine like terms in both sides

    3x < 12.


Divide both sides by 3.  You will get an equivalent inequality

    x < 4.


This last inequality determines the solution set, which is all rel numbers that are less than 4.


<U>ANSWER</U>.  The solution set is  {x < 4}, i.e. all real numbers that are less than 4.

         In the interval form, the solution is  ({{{-infinity}}},{{{4}}}).
</pre>

Solved.


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The standard solution procedure of solving such inequalities is collecting the terms with the unknown 
in one side of the inequality and collecting constant terms in the other side; 
then combining the like terms in each side and expressing the unknown variable in form of inequality.



If you want to see other examples on solving similar inequalities, &nbsp;look into the lesson

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

in this site.


Learn the subject from there.