Student Question

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

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...

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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.

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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.