document.write( "Question 80055: Please help me solve $\"+8%3C=-3x%2B1%3C=11\"$ \n" ); document.write( "

Algebra.Com's Answer #57426 by bucky(2189) $\"\"$ $\"About$

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$\"+8%3C=-3x%2B1%3C=11\"$
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\n" ); document.write( "You can solve this by using the same basic rules as you would in solving an equation,
\n" ); document.write( "with the exception that if you multiply or divide by a negative number, you must reverse
\n" ); document.write( "the direction of the inequality signs. In particular, whatever operation you do on one
\n" ); document.write( "section of the trichotomy, you must do the same operation on both of the other sections.
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\n" ); document.write( "Don't forget that we are trying to solve for +x. Therefore, we need to reduce the center
\n" ); document.write( "section of this inequality down to +x.
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\n" ); document.write( "So let's get rid of the +1 in the center section by subtracting +1 from all three sections.
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\n" ); document.write( "When we do that subtraction we get:
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\n" ); document.write( " $\"7%3C=-3x%3C=10\"$
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\n" ); document.write( "Now to isolate +x in the center section of the inequality, let's divide all three sections
\n" ); document.write( "by -3. And when you divide by that negative number, remember that you have to reverse
\n" ); document.write( "the direction of the inequality arrows.
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\n" ); document.write( " $\"7%2F%28-3%29%3E=x%3E=10%2F%28-3%29\"$
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\n" ); document.write( "In a little more standard use of signs this becomes:
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\n" ); document.write( " $\"-7%2F3%3E=x%3E=-10%2F3\"$
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\n" ); document.write( "That's the answer ... on a number line x must lie to the left of $\"-7%2F3\"$ but must be
\n" ); document.write( "to the right of $\"-10%2F3\"$ . Let's try a number in that span and see if it works.
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\n" ); document.write( "How about letting x equal -3. That number is between $\"-7%2F3\"$ and $\"-10%2F3\"$ so it
\n" ); document.write( "should satisfy the inequality. Start with:
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\n" ); document.write( " $\"+8%3C=-3x%2B1%3C=11\"$
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\n" ); document.write( "and substitute -3 for x to get:
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\n" ); document.write( " $\"+8%3C=%28-3%29%2A%28-3%29%2B1%3C=11\"$
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\n" ); document.write( "do the multiplication in the center section to get:
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\n" ); document.write( " $\"+8%3C=9%2B1%3C=11\"$
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\n" ); document.write( "do the addition in the center section and you find:
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\n" ); document.write( " $\"+8%3C=10%3C=11\"$
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\n" ); document.write( "As you can see, by letting x = -3 the inequality is satisfied.
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\n" ); document.write( "Try some other values outside the span that we found to see that they don't work.
\n" ); document.write( "For example, try letting x = -2 and then x = -4. These are outside the span that we
\n" ); document.write( "found in solving the equation.
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\n" ); document.write( "Hope this helps you to understand how to solve a trichotomy similar to this one. \n" ); document.write( "

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