document.write( "Question 70626: I need to solve the following inequalities and show on the real number line.
\n" ); document.write( "3(2-3x)>5[x-2(x+5)] \n" ); document.write( "

Algebra.Com's Answer #50416 by bucky(2189) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"3%282-3x%29%3E5%28x-2%28x%2B5%29%29\"$
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\n" ); document.write( "Start by treating this just as you would an equation and solve for x. First multiply out
\n" ); document.write( "the left side. When you do the result is:
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\n" ); document.write( " $\"6-9x%3E5%28x-2%28x%2B5%29%29\"$
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\n" ); document.write( "Next on the right side multiply out the -2 times (x+5). When you do the inequality
\n" ); document.write( "becomes:
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\n" ); document.write( " $\"6-9x%3E5%28x-2x-10%29\"$
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\n" ); document.write( "Then on the right side combine the x and -2x to get just -x. The inequality is then:
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\n" ); document.write( " $\"6-9x%3E5%28-x-10%29\"$
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\n" ); document.write( "Finally multiply out the right side:
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\n" ); document.write( " $\"6-9x%3E-5x-50\"$
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\n" ); document.write( "To cancel out the +6 on the left side, add a negative 6 to both sides. The inequality is
\n" ); document.write( "then\"
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\n" ); document.write( " $\"-9x%3E-5x-56\"$
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\n" ); document.write( "And to cancel out the -5x on the right side, add +5x to both sides. The result is:
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\n" ); document.write( " $\"-4x%3E-56\"$
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\n" ); document.write( "To solve this for positive x, divide both sides by -4. But now you have to remember the
\n" ); document.write( "rule ... whenever you divide or multiply both sides of an inequality by a negative number,
\n" ); document.write( "the inequality reverses direction. Dividing by -4 and reversing the inequality gives you:
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\n" ); document.write( " $\"x%3C14\"$
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\n" ); document.write( "This tells you that when x is less than 14 the inequality of the original problem is
\n" ); document.write( "satisfied. And when x is 14 or more, the inequality of the original problem will not work.
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\n" ); document.write( "Try a few values of x less than 14 and see if they don't work. Try x=14 and see why it doesn't
\n" ); document.write( "work. And try a value or two for x greater than 14 to verify that they don't work.
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\n" ); document.write( "Note 0 is less that 14, so you can try it. It makes all the x's disappear and the problem
\n" ); document.write( "is simplified because of that.
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\n" ); document.write( "Hope this helps you understand inequalities a little better. And don't forget the rule
\n" ); document.write( "about multiplying or dividing inequalities by a negative number. \n" ); document.write( "

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