math algebra question, really simple?

One way to deal with fractions is to multiply the entire equation by the denominator of a fraction that appears. So in this one, multiply the entire thing by 5. It won't change the equality.

(-1/5)y + 3x = 7

5 * [ (-1/5)y + 3x ] = 5 * 7

[ 5 * (-1/5)y ] + ( 5 * 3x ) = 35 . .[ using the distributive property on left-hand side ]

- y + 15x = 35 . . . . . . . . . . . . . . . . . .[ doing the multiplications on left-hand side ]

- y = 35 - 15x . . . . . . . . . . . . . . . . . . [ subtracted 15x from both sides ]

y = - 35 + 15x . . . . . . . . . . . . . . . . . .[ multiplied both sides by -1 ]

y = -5(7 - 3x) . . . . . . . . . . . . . . . . . . .[ factored out a -5 for some obscure reason ]

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So, you were right !

I personally may have written the final answer the following way, but remember that what I type here and what you came up with are equivalent expressions, i.e. they are the same.

After I got to

y = - 35 + 15x

I would have rewritten it as

y = 15x - 35 . . . . . . [ this is just rearranging terms in descending powers of x ]

Then I would have factored out a 5 , instead of as above where we factored out a -5

y = 5(3x - 7)

That's how I would have presented the answer, but like I said, it's the same as the other way of writing it.