### Video Transcript

The height of a wall is
increased by one-sixth. The new height of the wall is 4.2
metres. Calculate the original height of
the wall.

We have a wall whose height is
increased by one-sixth. And then, the new height of the
wall is 4.2 metres. And we want to calculate 𝑥, the
original height of the wall.

If 𝑥 is the original height, then
𝑥 multiplied by some multiplier will equal our new height. We can plug in 4.2 for the new
height. Bring down our 𝑥.

Looking back at our diagram, the
original height of the wall can be written as a fraction of one, six over six. And that means our multiplier will
be the six-sixths from the original height plus the one-sixth increase. Our multiplier is
seven-sixths.

So seven sixths 𝑥 equals 4.2. To solve for 𝑥, we’ll need to get
it by itself. We can do that by multiplying
seven-sixths 𝑥 by six over seven. And if we do that on the left of
our equation, we have to do it on the right side as well.

On the left, everything cancels out,
leaving us with 𝑥. On the right side, 4.2 times six
and then divided by seven equals 3.6.

The original height of the wall was
3.6 meters.