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Let x be the unknown number.
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\n" ); document.write( "Then 2 times the unknown number is 2*x.
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\n" ); document.write( "Increase that by 28 and you have 2*x + 28
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\n" ); document.write( "This is to be less than or equal to 6 times the unknown number ... or less than or equal to 6*x.
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\n" ); document.write( "In inequality form this is:
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\n" ); document.write( "We need to solve this for x. So we need to collect the terms containing x on one side of the
\n" ); document.write( "inequality and all the numbers on the other side. Start by getting rid of the +28 on the
\n" ); document.write( "left side of the inequality. Do this by subtracting 28 from the left side. But when you
\n" ); document.write( "do that subtraction you also have to subtract 28 from the right side. This makes the inequality
\n" ); document.write( "become:
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\n" ); document.write( "Now get rid of the 6*x term on the right side by subtracting 6*x. But when you subtract 6*x
\n" ); document.write( "from the right side, you must also subtract 6*x from the left side. This subtraction
\n" ); document.write( "from both sides simplifies the equation to:
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\n" ); document.write( "Finally, to solve for +x divide both sides of the inequality by -4 which is the multiplier
\n" ); document.write( "of x. Now an important rule comes into play. When you divide or multiply both sides of
\n" ); document.write( "an inequality BY A NEGATIVE QUANTITY the inequality arrow must CHANGE DIRECTION.
\n" ); document.write( "So this division by -4 causes several major changes. The -4x becomes just x and the -28
\n" ); document.write( "becomes +7. And also the inequality arrow switches direction. Substituting all these
\n" ); document.write( "changes into the equation results in:
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\n" ); document.write( "So on the number line, x must be +7 or be to the right of +7. Let's try a value just to
\n" ); document.write( "convince ourselves that this answer is correct. Let's set x equal to +8 which is to
\n" ); document.write( "the right of +7 on the number line. If you return to the original problem and set x equal
\n" ); document.write( "to +8 the original problem statement becomes:
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\n" ); document.write( "2 times 8 is 16 and increased by 28 is 44. That must be less than or equal to 6 times 8 which is 48.
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\n" ); document.write( "That works. How about we try a value of x that is less than 7 ... say x = 6.
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\n" ); document.write( "2 times 6 is 12 and increased by 28 is 40. That must be less than or equal to 6 times 6 which is 36.
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\n" ); document.write( "This does not work. These couple of spot checks serve to convince us that our answer
\n" ); document.write( "looks good ... x must be greater than or equal to +7.
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\n" ); document.write( "Hope this helps you to understand inequality problems a little more. And don't forget
\n" ); document.write( "the rule that if you multiply or divide both sides of an inequality by a negative number
\n" ); document.write( "you must reverse the direction of the inequality arrow. \n" ); document.write( "