SOLUTION: Water is in liquid state if its temperature, t(in degrees celsius), satisfies t-50<50. find the two solutions of t-50=50.what do the solutions represent? please help really confuse

Question 91604: Water is in liquid state if its temperature, t(in degrees celsius), satisfies t-50<50. find the two solutions of t-50=50.what do the solutions represent? please help really confused never seen this before.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
I believe this problem should be that for water in a liquid state the Celsius temperature
must satisfy the equation:
.

.
The absolute value signs mean that whatever is within the signs will be a positive value whether
the quantity is negative or positive.
.
To solve this equation you form two equations ... one equation by treating the quantity inside
the absolute value signs as positive and another equation by treating the quantity inside the
absolute value signs as negative.
.
One other rule that applies to inequalities is that you can solve them using the rules and
processes that apply to equations with the exception that if you multiply or divide both
sides by a negative quantity you need to reverse the direction of the inequality.
.
Let's apply this process to the equation of this problem. First, let's form an inequality
by treating the quantity inside the absolute value signs as a positive quantity. With this
process the inequality becomes:
.

.
Solve by getting rid of the -50 on the left side by adding +50 to both sides. This makes
the inequality become:
.

.
After the addition the inequality simplifies to:
.

.
This is one answer. We will return to it in a bit. But first, let's set up a second
inequality by treating the quantity inside the absolute value signs as a negative
quantity. When you do, the inequality becomes:
.

.
get rid of the minus sign on the left by multiplying both sides by -1. And don't forget the
rule that if you multiply (or divide) both sides of an inequality by a negative, you reverse
the direction of the inequality sign. So multiplying this inequality by -1 makes it become:
.

.
Solve this by adding +50 to both sides to get:
.

.
This is the second answer.
.
So looking at our two answers we have and and this tells us that
for water to be in the liquid state the Celsius temperature range of the water must be
between 0 degrees C and 100 degrees C. On the Celsius scale of temperatures, at 0 degrees C
water freezes to ice and at 100 degrees C it boils and changes to steam. Therefore,
again, if water is above 0 degrees C but below 100 degrees C it will be in the liquid
state.
.
Hope this helps you to understand the problem and what it means. And hope the discussion
of absolute value quantities makes some sense to you also.

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