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Originally Posted by mstcrow5429
If I'm finding X, and I have -1/2x + 3 = 1, I multiply each side by 2/1. However, if I have 1/2x + 3 = 1, I multiply each side by 2/1, not -2/1, correct? I think I'm missing a basic connection here. Thanks.
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Remember that whatever you multiply to one side of the equation, you must multiply to the other. In other words, you can multiply -2/1 or 2/1 to both problems as long as you do the same to the other side of the equation. DixieGirl showed you one way, so let's try it the other way:
1/2x + 3 = 1
Multiply -2/1 to both sides (-2/1)(1/2x +3) = (-2/1)1
Negative signs on both sides -x - 6 = -2
Add +6 to both sides -x= 4
Multiply -1 to both sides to cancel negative on "x" (-1)(-x) = (-1)(4)
This equals
x = -4 Answ.
Try this one:
-1/2x + 3 = 1
Multiply -2/1 to both sides (-2/1)(-1/2x + 3) = (-2/1)1
Negative signs cancel on left side x - 6 = -2
Add +6 to both sides
x = 4 Answ.
These are the same answers DixieGirl came to. The only difference is that I multiplied by a negative 2/1 instead of a positive 2/1. As long as you do the same thing to both sides, it doesn't matter which number you use, mathematically.
Food for thought:
Problem: -1/2x + 3 = 1
Multiply both sides by 6: 6(-1/2x + 3) = 6(1)
Equals -3x + 18 = 6
Now, add -18 to both sides: -3x = -12
Divide both sides by -3:
x=4, Answ.
The answer is still 4, even though at the beginning you multiplied both sides by 6!
Hope this helps!