### Video Transcript

Solve 𝑥 plus three over five
equals 10.

We know that 𝑥 plus three over
five equals 10. And to solve for 𝑥, we need to get
it by itself. We need to isolate it. And that means we need to undo the
operations that are being done to 𝑥. In the numerator, we have some
number 𝑥 plus three. And whatever that number plus three
is is being divided by five. And that means to find out what
that number is, we first need to undo this division.

And we can do that by multiplying
by five. But if we multiply by five on the
left, we need to multiply by five on the right. On the left, the five in the
numerator and the five in the denominator cancel out, leaving us with 𝑥 plus
three. And on the right, we have 10 times
five, which is 50. And now, we have a simple equation,
𝑥 plus three equals 50. So, we subtract three from both
sides. And we get 𝑥 equals 47.

Why couldn’t we subtract three from
both sides? What would happen if we did? On the left, we would have 𝑥 plus
three over five minus three. And on the right, we would have
seven. Now, this is still a true
statement. 𝑥 plus three over five minus three
does equal seven. However, we’re no closer to solving
for 𝑥. And that’s because the entire
numerator is being divided by five. And we can’t take this plus three
out of the numerator. This is because we have to reverse
the operations in the contrary order than when we started.