Question 80895
You can work problems of this type just as you would solve an equation with the exception that
if you divide or multiply by a negative quantity, then you must reverse the direction
of the inequality sign.
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So let's start with the given expression:
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{{{3a + 8/2 < 10}}}
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Notice that {{{8/2 = 4}}} so we can replace it by 4 to get:
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{{{3a + 4 < 10}}}
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Get rid of the 4 on the left side by subtracting 4 from both sides of the inequality
to get:
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{{{3a < 6}}}
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Now reduce the left side to just "+a" by dividing both sides of the inequality by +3
to get:
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{{{a < 6/3}}}
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which simplifies to {{{a < 2}}}
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The original inequality should be satisfied as long as the value of "a" is less than 2.
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Let's build our self confidence by trying some values for "a".  Suppose we let "a" equal
zero. That value is obviously less than +2. If we substitute zero for a in the original
inequality we get:
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{{{3a + 8/2 < 10}}} which becomes {{{0 + 4 < 10}}}. That works. Similarly, if we let a = +1
the original inequality becomes:
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{{{3*1 + 8/2 < 10}}} and this further simplifies to {{{3 + 4 < 10}}}. That works also.
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Now let's set a = +3.  That is outside the limit we found since +3 is not less than +2.
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With a = +3 the original inequality becomes:
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{{{3*3 + 8/2 < 10}}}. This simplifies to {{{9 + 4 <10}}}, and this obviously is not true.
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From these spot checks, it seems as though our answer is correct.
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Hope this helps you to understand the problem.
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Cheers.