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|-2v+8|=6 solve each equation

User Ratkok
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1 Answer

4 votes

Answer:

v = 1 or v = 7

Explanation:

By "or", I mean there's two solutions.


-2v+8=-6\quad \mathrm{or}\quad \:-2v+8=6

Because we are doing negative and positive values, that may create a logical gap between our answers, so that would only make it worse, right? But to patch that gap, we separate the problems into having two different solutions so they will be mathematically correct. The only way for v to equal 7 and get negative 6 is for v to be positive, and v would need to be multiplied by 2. Since the equation is equal to positive 6 without v, we now know we only need to substitute 7 for v in respect for negative 6. This way, the first equation becomes true; v = 7

For part 2, there is only one other value for v, and we know that it can't be 7 if we're dealing with positive 6 this time. Instead, the number would be closer to zero. If the inverse of adding is subtraction, think of adding negatives to positives as the co-inverse of addition. This way, that makes it seem as though we are subtracting 2 from 8 even though that's not the case. Now, we first substitute v for 1 automatically since v cannot equal zero. Now, we multiply negative 2 by positive 1, which gives us negative 2 again. Any number multiplied by 1 stays the same, regardless. Lastly, you add negative 2 to positive 8, and that gives you 6, which would mean the second solution has been found; which is v = 1

Hope this helps! Have a good day.

User Vitor Braga
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