Discussion





Solve inequalities just like you would solve equations.  There are two very

important differences.



1.  Instead of a single element in the solution set that you would get with

a linear equation in a single variable, with an inequality you get a solution

set with an infinite number of elements represented by a number line interval.





2.  When, in the process of solving the inequality, you need to multiply or

divide by a negative number, you must reverse the sense of the inequality.

Here's why:





, but  because .







Solution











Just like an equation, you can add the same value to both sides:













Therefore, the solution set is all real numbers such that 











Check Answer





The solution interval says that  is a solution, so check:

Is  a true statement?  Yes, 





The solution interval implies that anything smaller than 16 is a solution:

Is  a true statement?  Yes, 





The solution interval implies that anything larger than 16 is NOT a solution:

Is  a false statement?  Yes, 12 is NOT less than or equal to 11.





Answer checks.

 

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
 d - 5 ≤ - 11 

Add 5 to both sides to the inequality to get:

d <= -6

=============

Cheers,

Stan H. 

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