Seven more than means to add 7.

It will be added to whatever follows the words "more than". Here it is the rest of the phrase: "three times a number".

Either (7 + 3x) or (3x + 7) is correct because addition is commutative.

Let's change one word in the original phrase. Let's change "more" to "less":

" seven less than three times a number"

"seven less than" means to subtract 7.

As before, it is the description following "than".

3x - 7 is the translation of "seven less than three times a number".

Notice how the order of the algebra is different from the order of the words. We say the words with the "seven less than" first, but have to write the "- 7" as the second term. Order matters in subtraction.

Example 2: Now consider a phrase mentioning two numbers.

"There are two numbers, the larger of which is four more than three times the smaller."

We want to represent the numbers in terms of one variable, "x".

Since the larger number is described in terms of the smaller number, it is clearer to use "x" as the smaller number.

"three times the smaller" involves multiplication of 3 and x.

"more than" involves addition.

Either 4 + 3x or 3x + 4 describes the larger number.

Now let's try a phrase which describes three numbers:

"There are three numbers. The middle number is 5 times the smallest, and the largest number is 8 more than the middle number."

Since the smallest number is used to describe the middle one, and the middle one is used to describe the largest one, a good choice for "x" is the smallest number.

The word "times" means multiplication, so the middle number is 5x.

Since the middle number is 5x, we need to add 8 to it to get 8 + 5x.