Write an equation that describes the statement “When two is subtracted from 𝑦, the result is the same as when four is added to 𝑥, and the result is multiplied by three.”
So we’ve been given a statement in words and we’re asked to write it as an equation. So we need to translate it into algebra. Let’s look at each stage of the statement in turn.
The statement begins with “when two is subtracted from 𝑦.” So if we start with 𝑦 and then subtract two from it, this gives the algebraic expression 𝑦 minus two. The statement continues that the result is the same as when four is added to 𝑥 first of all. So if we start with 𝑥 and then we add four, we have the algebraic expression 𝑥 plus four.
The statement continues that the result is multiplied by three. So that would be three multiplied by the result, which was 𝑥 plus four. And we need the brackets here because we need to show that the three is multiplying both the 𝑥 and the four. We don’t, however, need the multiplication sign in this algebraic expression. So we can just write it as three and then brackets 𝑥 plus four.
Now the middle part of the statement said that the result is the same, which means that the expression we got for the first part must be equal to the expression we’ve written for the second part. So we can write our equation as our first expression, 𝑦 minus two, is equal to our second expression, which is three lots of 𝑥 plus four. The equation that describes the given statement is 𝑦 minus two equals three brackets 𝑥 plus four.