SOLUTION: Sole each inequality. State the solution set interval notation and sketch its graph! 1/6

SOLUTION: Sole each inequality. State the solution set interval notation and sketch its graph! 1/6 - 1/3 t > 0 Please Help :(

Question 90385: Sole each inequality. State the solution set interval notation and sketch its graph!
1/6 - 1/3 t > 0

Please Help :(
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The goal in this problem is to solve for t. You can do this by basically using the same rules
and procedures as you would for solving an equation with two exceptions. First, you replace
the equal sign of an equation with the inequality sign, and Second if you divide or multiply
the inequality by a minus quantity, then you reverse the direction of the inequality
sign.
.
That being said, let's do the problem:
.
Given:
.
As you would do with an equation, get rid of the on the left side by subtracting
from both sides. When you do that the inequality becomes:
.

.
Get rid of the denominators by multiplying both sides of the equation by +6. When you
do that the equation becomes:
.

.
By dividing the denominators into the numerators on both sides, you simplify the equation to:
.

.
Finally, you can now solve for t by dividing both sides of the inequality by -2. However,
don't forget the rule about multiplying or dividing both sides by a NEGATIVE quantity.
Because of this rule, when we divide both sides by -2, we need to reverse the direction of
the inequality sign. Dividing by -2 results in:
.

.
and reversing the direction of the inequality sign makes it:
.

.
Now doing the actual division by -2 simplifies the equation to:
.

.
This tells us that for the original problem, as long as t is less than the inequality
will be true.
.
You can verify this by going to the original inequality and substituting
for t. You get:
.

.
Doing the multiplication results in:
.

.
and this reduces to
.

.
This is obviously not true. But suppose we make t less than . Will the inequality then
be true? Let's set t = 0 which is obviously less than . When t is 0 the inequality
becomes:
.

.
This simplifies to:
.

.
This is obviously true. So it lends support to our answer that if t is less than the
original inequality will be true.
.
Hope this helps you to understand the problem a little more.

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