Question 123241
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Discussion
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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:


{{{2<3}}}, but {{{(-1)(2)>(-1)(3)}}} because {{{-2>-3}}}.
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Solution
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{{{d-5<=11}}}


Just like an equation, you can add the same value to both sides:
{{{d-5+5<=11+5}}}


{{{d<=16}}}


Therefore, the solution set is all real numbers such that {{{-infinity<d<=16}}}


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Check Answer
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The solution interval says that {{{d=16}}} is a solution, so check:
Is {{{16-5<=11}}} a true statement?  Yes, {{{11<=11}}}


The solution interval implies that anything smaller than 16 is a solution:
Is {{{10-5<=11}}} a true statement?  Yes, {{{5<=11}}}


The solution interval implies that anything larger than 16 is NOT a solution:
Is {{{17-5<=11}}} a false statement?  Yes, 12 is NOT less than or equal to 11.


Answer checks.
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