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additive inverse = -x
so when -x/12 = (1/3)(1/x)
solve for x.
The wording for
"same one as less than 3 times"
is iffy, but if you take it the way I did, then your number is a complex number:
I think the problem might have been worded as "...same as one less than three times ..."
If that's the case, then your answer won't be imaginary.
Let the number be x.
Then “the additive inverse” is –x, because –x + x = 0.
Also, the “reciprocal” is 1/x.
These are math terms that show up often.
So it says “the additive inverse of a number divided by 12 ...”
Well, that’s just –x/12.
“... is the same as one less than 3 times its reciprocal.”
Three times the reciprocal is 3*(1/x) = 3/x.
And one less than that is 3/x – 1.
So that means that –x/12 is equal to 3/x – 1.
So we want to solve –x/12 = 3/x – 1.
You can solve this on your own from this point.
If you’re having a hard time with that, then look below.
-x/12 = (3-x)/x by combining the fraction on the Right Hand Side.
We want to do this to be able to “cross-multiply”.
In other words, we now have an equation with fractions, and we’d like to
reduce it down to an equation without fractions.
If we multiply both sides by 12,
we’d get rid of the denominator 12 on the Left Hand Side.
If we multiply both sides by x,
we’d get rid of the denominator x on the Right Hand Side.
Doing that, we see that -x/12 = (3-x)/x
is equivalent to –x^2 = 36 – 12x.
So we want to solve for x in x^2 – 12x + 36 = 0.
That factors as (x – 6)^2 = 0.
So x = 6 is our answer.
And to check, we can go back and plug in 6 into our original equation –x/12 = 3/x – 1.