Question 118198
Given:
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{{{(y - 3)/2 > 1/2 - (y-3)/4}}}
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To make things easier, get rid of the denominators by multiplying both sides (all terms) by +4.
This multiplication becomes:
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{{{(4*(y - 3))/2 > (4*1)/2 - (4*(y-3))/4}}}
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In each term divide the denominator into the +4 multiplier. This eliminates each of the denominators
and reduces the problem to:
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{{{(2*(y - 3)) > (2*1) - (1*(y-3))}}}
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Do the indicated multiplications in each of the three terms:
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{{{2y - 6 > 2 - y + 3}}}
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Get rid of the -6 on the left side by adding +6 to both sides:
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{{{ 2y > 2 - y + 3 + 6}}}
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Get rid of the -y on the right side by adding +y to both sides:
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{{{ 3y > 2 + 3 + 6}}}
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Add all the terms on the right side:
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{{{3y > 11}}}
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Solve for y by dividing both sides by 3:
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{{{y > 11/3}}}
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This answer tells you that the original inequality will be true as long as y is greater than {{{11/3}}}.
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Let's check. Suppose that y equals 4. That value is greater than 11/3, so when y  equals 4,
the inequality should be true. Take the original inequality and substitute +4 for y ...
The original inequality is:
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{{{(y - 3)/2 > 1/2 - (y-3)/4}}}
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When you substitute +4 for y, it becomes:
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{{{(4 - 3)/2 > 1/2 - (4-3)/4}}}
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The left side reduces to {{{1/2}}} and on the right side the negative term reduces to {{{-1/4}}}.
This makes the inequality become:
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{{{1/2 > 1/2 - 1/4}}}
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Subtract {{{1/2 }}} from both sides and you have:
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{{{0 > -1/4}}}
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This is true. Zero is greater than {{{-1/4}}} because 0 is to the right of {{{-1/4}}} on the
number line.
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Now try a value of y that is less than {{{11/3}}}. Suppose you let y = 3. That is less than {{{11/3}}}.
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Start with the original inequality:
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{{{(y - 3)/2 > 1/2 - (y-3)/4}}}
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Substitute 3 for y and this inequality becomes:
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{{{(3- 3)/2 > 1/2 - (3-3)/4}}}
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The numerator on the left side and also the numerator of the negative term on the right side
both become zero. So the inequality becomes:
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{{{0 > 1/2 - 0}}}
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The right side reduces to {{{1/2}}} so the inequality is:
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{{{0 > 1/2}}}
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This is NOT true ... zero is not greater than 1/2. So choosing a value for y that is less
than {{{11/3}}} did not work. 
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From this "quick trial" it appears that y must be greater than {{{11/3}}} is a good answer.
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Hope this helps you to understand the problem and how to solve it ...
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