Question 558280: (2/3)u + 8 = 2
If I work the problem out like it shows in the examples I get 0. How do I know that u=-9?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The variable  was first multiplied by the fraction 2/3, and to the result, the number 8 was added.
You are trying to find the original number, . It could be a negative integer. It could be a fraction, even a negative one.
To solve this type of equation you have to undo what was done to the variable (u, in this case) in reverse order.
Before going to bed, I'll take of my shoes first, and then I'll take off my socks, undoing what I did this morning in reverse order.
To undo the adding of 8, I can subtract 8, which I like to think of as adding the number (-8).
The expressions on both sides of the equal sign are equal. If I add the number (-8) to both sides, the results will still be equal. That step is reversible too, so the old equation and the new equation are equivalent and will have exactly the same solution(s).
Simplifying:
To undo the multiplication times 2/3, we have to divide by 2/3, which is really multiplying by 3/2.
Multiplying both sides of the equal sign times 3/2 results in an equivalent equation
 -->  -->  --> 
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