Twice A Number

What does the phrase "Twice a number x" mean? Why do we replace numbers with letters/symbols?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The number "x" is represented as a letter because it is a variable. This is the idea of the type of math that is named algebra. Replacing the variables with single letters (sometimes English alphabet, sometimes Greek alphabet - because the Greeks had a big role in inventing algebra, so we still use their alphabet today) is a shorthand. When we work with long or complicated expressions involving one or more variables, this shorthand makes it easier to follow through the steps on paper at a glance, concentrating it down to the real essentials. It also saves on ink and time!

An example of a variable that "x" might represent is the number of oranges a boy called Sam eats in a week. If his friend Jenny always eats twice as many oranges in a week as Sam, then we can say that she eats "2x" oranges in a week. It is a variable because it varies each week, but the relationship between what the two friends eat always stays the same. You can see that "x" is a shorthand way of saying "number of oranges eaten per week". It is like when you write $ to mean United States Dollars. It makes comparing prices at a glance easier.

Approved by eNotes Editorial Team
An illustration of the letter 'A' in a speech bubbles

Translate the written/verbal expression "twice a number x" into mathematical/symbolic notation:

Twice a quantity usually indicates to take two of the things in question; usually this indicates to multiply by 2.

Thus "twice a number x" can be written symbolically as 2x.

If this is part of a problem, say twice a number x is 6, then we can rewrite algebraically as 2x=6; dividing both sides by 2 yields x=3. And we can see that, indeed, twice the number 3 is 6 as required. In the expression "twice a number x is 6" twice indicates to multiply by 2, the multiplicand (the thing multiplied by the multiplier 2) is x, and the word "is" can be expressed by the equals sign.

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial Team