SOLUTION: A number decreased by the difference between six and the product of the number and four. The sum of eight more than a number and one-third of the number

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Question 568474: A number decreased by the difference between six and the product of the number and four.
The sum of eight more than a number and one-third of the number
Answer by AnlytcPhil(1806) (Show Source):
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A number decreased by the difference between six and the product of the number and four.

Replace the words "a number" and "the number" by x.

x decreased by the difference between six and the product of x and four.

Replace the words "the product of x and four" by 4x

x decreased by the difference between six and 4x.

Replace the words "the difference between six and 4x" by (6-4x)

x decreased by (6-4x).

Replace the words "decreased by" by a minus sign - .

x - (6-4x)

Remove the parentheses. It's preceded by a - sign so the signs change:

x - 6 + 4x

Combine like terms:

5x - 6
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The sum of eight more than a number and one-third of the number

Replace the words "a number" and "the number" by x.

The sum of eight more than x and one-third of x.

Replace the words "one-third of x" by x

The sum of eight more than x and x.

Replace the words "eight more than x" by (x+8).

The sum of (x+8) and x.

Replace that by

(x+8) + x

Remove the parentheses:

x + 8 + x

Get an LCD of 3 and write x as , 8 as , and x as :

+ +

Combine the fractions:

Combine like terms on top:

You can factor 4 out of the numerator if you like:

but it isn't necessary. You can also write it as

(x+6)

but that isn't necessary, either.
You can also distribute that and get

x + 8

but that isn't necessary, either.
Edwin