### Video Transcript

I think of a number. I multiply it by three and then subtract
five. The answer is 13. What number did I think of?

One way to answer this question is to set
up an equation. We can begin by letting the number being
unknown, in this case, 𝑥. We are told that we multiply the number
by three. This can be written as three 𝑥. We then subtract five, so our expression
is three 𝑥 minus five. As the answer is 13, we can turn this
expression into an equation by setting it equal to 13. We can now work out the number by solving
this equation. We can do this using the balancing method
and inverse operations.

The inverse or opposite of subtracting
five is adding five. Adding five to both sides of the equation
gives us three 𝑥 equals 18 as negative five plus five is zero and 13 plus five is 18. Our final step is to divide three from
both sides of this new equation as division is the inverse of multiplication. Three 𝑥 divided by three is equal to 𝑥,
and 18 divided by three is equal to six. This means that the number that was
initially thought of was six. We can check this answer by multiplying
six by three and then subtracting five. As this does indeed give us an answer of
13, we know that the answer is correct.

An alternative method that could’ve been
used in this question is using function machines. Once again, we start with the unknown
𝑥. We multiply it by three, subtract five,
and end up with the answer 13. We can reverse this by carrying out the
inverse operations. The inverse or opposite of subtracting
five is adding five. And the inverse of multiplying by three
is dividing by three. 13 plus five is equal to 18. Dividing this by three gives us an answer
of six. We have once again proved that the
original number was six.