SOLUTION: i need help with understanding how to solve inequalities and graph its solutions example -3>-3+k i dont want just the answer i want to know how you came up with the answer

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Question 238164: i need help with understanding how to solve inequalities and graph its solutions example -3>-3+k i dont want just the answer i want to know how you came up with the answer
Found 2 solutions by Theo, College Student:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
your equation is -3 > -3+k

you solve inequality equations the same way you solve equality equations.

the only difference is that when you multiply both sides of the equation by a negative number, then the inequality reverses.

example:

5 > 3

multiply both sides of this equation by -1 to get:

-5 < -3

the inequality reversed as can easily be seen.

5 is definitely greater than 3.

-5 is definitely smaller than -3

your equation is:

-3 > -3 + k

add 3 to both sides of this equation to get:

0 > k

this is the same as k < 0 as I will now show.

your equation is:

0 > k

subtract k from both sides of this equation to get:

-k > 0

multiply both sides of this equation by -1 to get:

k < 0

that's how it's done.

Answer by College Student(505) (Show Source):
You can put this solution on YOUR website!
When we have an inequality or equality, we need to isolate the variable in order to find its value.
.
When we add or sustract from both sides of the inequality, the inequality symbol remains the same.
However, when we multiply or divide a NEGATIVE value on both sides, the inequality symbol changes direction.
.
It also changes direction if we decide to swap one side for the other.
Here are a few examples:
.
Sum operation:

If you decide to swap sides, then you'd say: to maintain the same result.
================
Negative Multiplication operation:

...same as to say...
Positive Multiplication operation:

...same as to say...
===============================================
Now, let's work on your problem:
...add 3 on both sides to leave k alone, you get:

...same as to say...
Done! Keep posting problems if you need more help. :)