SOLUTION: Please help with the following inequality. I have the problem and the answer but nothing in between. (y-3)/2 > 1/2 - (y-3)/4 interval notation: (11/3, %) Thanks for your

Question 118198: Please help with the following inequality. I have the problem and the answer but nothing in between.
(y-3)/2 > 1/2 - (y-3)/4 interval notation: (11/3, %)
Thanks for your help just can't seem to get this question. It's the only problem in my unit lesson I couldn't complete.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
To make things easier, get rid of the denominators by multiplying both sides (all terms) by +4.
This multiplication becomes:
.

.
In each term divide the denominator into the +4 multiplier. This eliminates each of the denominators
and reduces the problem to:
.

.
Do the indicated multiplications in each of the three terms:
.

.
Get rid of the -6 on the left side by adding +6 to both sides:
.

.
Get rid of the -y on the right side by adding +y to both sides:
.

.
Add all the terms on the right side:
.

.
Solve for y by dividing both sides by 3:
.

.
This answer tells you that the original inequality will be true as long as y is greater than .
.
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:
.

.
When you substitute +4 for y, it becomes:
.

.
The left side reduces to and on the right side the negative term reduces to .
This makes the inequality become:
.

.
Subtract from both sides and you have:
.

.
This is true. Zero is greater than because 0 is to the right of on the
number line.
.
Now try a value of y that is less than . Suppose you let y = 3. That is less than .
.
Start with the original inequality:
.

.
Substitute 3 for y and this inequality becomes:
.

.
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:
.

.
The right side reduces to so the inequality is:
.

.
This is NOT true ... zero is not greater than 1/2. So choosing a value for y that is less
than did not work.
.
From this "quick trial" it appears that y must be greater than is a good answer.
.
Hope this helps you to understand the problem and how to solve it ...
.

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