SOLUTION: Please help me solve {{{ 8<=-3x+1<=11}}}

Question 80055: Please help me solve
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!

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You can solve this by using the same basic rules as you would in solving an equation,
with the exception that if you multiply or divide by a negative number, you must reverse
the direction of the inequality signs. In particular, whatever operation you do on one
section of the trichotomy, you must do the same operation on both of the other sections.
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Don't forget that we are trying to solve for +x. Therefore, we need to reduce the center
section of this inequality down to +x.
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So let's get rid of the +1 in the center section by subtracting +1 from all three sections.
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When we do that subtraction we get:
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Now to isolate +x in the center section of the inequality, let's divide all three sections
by -3. And when you divide by that negative number, remember that you have to reverse
the direction of the inequality arrows.
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In a little more standard use of signs this becomes:
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That's the answer ... on a number line x must lie to the left of but must be
to the right of . Let's try a number in that span and see if it works.
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How about letting x equal -3. That number is between and so it
should satisfy the inequality. Start with:
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and substitute -3 for x to get:
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do the multiplication in the center section to get:
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do the addition in the center section and you find:
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As you can see, by letting x = -3 the inequality is satisfied.
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Try some other values outside the span that we found to see that they don't work.
For example, try letting x = -2 and then x = -4. These are outside the span that we
found in solving the equation.
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Hope this helps you to understand how to solve a trichotomy similar to this one.
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