Phrases into Expressions

Most equations start as a sentence in words. The first step is to turn a phrase into an expression. Call the unknown quantity a letter, then translate the words around it.

"The sum of", "more than" and "increased by" mean add. "The difference", "less than" and "decreased by" mean subtract. "Twice", "three times" and "the product of" mean multiply. "Half of", "divided by" and "per" mean divide.

Take the phrase "5 more than twice a number". Call the number $n$. Twice the number is $2n$. Then 5 more than that is $2n+5$. The phrase "7 less than a number" is $n-7$, not $7-n$, because "less than" reverses the order of the words. "Half of a number, plus 1" is $\frac{n}{2}+1$.

The order inside a sum does not matter. The expressions $2n+5$ and $5+2n$ are the same, so either one is a correct translation.