Is 1/8 - 10 (3/4-3/8x) + 5/8x equivalent to -1/8(59-35x)explain your answer.

Yes!

Step-by-step explanation:

Lets start with 1/8 - 10 (3/4-3/8x) + 5/8x and try to simplify it:

1/8 - 10 (3/4-3/8x) + 5/8 x = ?

Apply distributive and multiply the inside terms by 10 that is outside the parenthesis:

1/8 - [10*(3/4) - 10(3/8)x] +5/8 x = 1/8 - [30/4 - 30/8 x] +5/8 x

We can now drop the parenthesis:

1/8 - 30/4 + 30/8 x +5/8 x =

Now we put together terms with and without x:

[ 1/8 - 30/4] + [30/8 x + 5/8 x] =

Multiply and divide the 30/4 term by 2 to make an 8 appear in the denominator:

[1/8 - 2*(30)/2*(4)] + [30/8 x  + 5/8 x] =

[1/8 - 60/8] + [30/8 x + 5/8 x] = -59/8 + 30/8 x + 5/8 x  = -59/8 + 35/8 x

Taking -1/8 as common factor in both terms:

= -1/8 [ -59 - 35 x]

So, we can confirm that:

1/8 - 10 (3/4-3/8x) + 5/8 x = -1/8 [ -59 - 35 x]

YES, the terms are equivalent!

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