SOLUTION: 8-6x>2-5x

Question 404947: 8-6x>2-5x
Answer by IWork4Dessert(60) (Show Source): You can put this solution on YOUR website!
Your ultimate goal here is to get the variable(x) alone on one side of the equation with an answer on the other.
8-6x>2-5x
The first thing to do is to get rid of the integers without variables on one side. It doesn't matter which side you want to isolate the variable on, but no matter which it is, make sure that the variable is totally alone, without a coefficient(the number in front of a variable).
So let's just choose that we want the variable to be on the left side. Start by getting rid of the number on the left side.
8-6x>2-5x
-8 -8
You want to get rid of the variable by adding or subtracting it from the number on the other side. That transfers the number over. Note: You decide whether to add or subtract by choosing the opposite sign as the one on the number.
Example: -10-5x<6+3x
+10 +10
Now that you've gotten rid of the number on the left, your equation looks like this:
-6x>-6-5x
The next step is to transfer the variable on the right side of the equation over to the left. You do this the same way that you transfer a number.
-6x>-6-5x
+5x +5x
Now you have your variable on the left and your number on the right, and there's no coefficient hanging on to the variable anymore.
-x>-6
However, your variable cannot have a negative sign on it. All you have to do to get rid of it is divide both sides of the equation by -1.
-x>-6
�-1 �-1
The trick here is that when you have an inequality(an equation with >, <, ≤, or ≥), you have to flip the sign in the middle around if you divide by a negative number.
This being said, you just need to turn the "greater than" sign around and make it a "less than" sign.
x>6
x<6
And there's your final answer.
x<6
NOTE: If you do end up with a coefficient still on your variable after transferring the variable over, you need to divide both sides of the equation by that number. Remember that dividing by a negative number results in a sign flip.
Example: -10-5x<6+3x
+10 +10
-5x<16+3x
-3x -3x
-8x<16
�-8 �-8
x>-2
Just in case you run across a problem like that.
Hope this helped.
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