Video: Changing the Subject of a Formula

Rearrange 𝑦 = 3𝑥 − 5 to make 𝑥 the subject.

01:46

Video Transcript

Rearrange 𝑦 equals three 𝑥 minus five to make 𝑥 the subject.

In order to rearrange a formula and change the subject, we need to use our knowledge of inverse operations and the balancing method. Our aim in this question is to get 𝑥 on one side of the equation and all other terms on the other side. The opposite or inverse of subtracting five is adding five. So we do this to both sides of the equation. The left-hand side becomes 𝑦 plus five and the right-hand side three 𝑥.

Our second and final step is to divide both sides of this new equation by three. On the left-hand side, we have 𝑦 plus five divided by three. On the right-hand side, three 𝑥 divided by three is 𝑥. The rearranged version of the equation with 𝑥 as the subject is 𝑥 equals 𝑦 plus five divided by three.

An alternative method here would be to consider function machines. If we let 𝑥 be the input and 𝑦 the output of the original equation, then 𝑦 equals three 𝑥 minus five means that we multiply 𝑥 by three and then subtract five. The inverse or opposite of these two steps are adding five and dividing by three. Once again, we get the answer 𝑥 is equal to 𝑦 plus five divided by three.

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