How do you solve for r in #4(r+3)=t#?
Why the shortcut method works:
Consider the following:
So it follows that
From this you can see that there is 4 lots of r and 4 lots of 3's
So when multiplying out the bracket we have the equivalent of
This is the same as:
We are told that we need to solve for r. That means we must end up with only one r in the equation and that it is to be on the left hand side of the equals sign. Everything else is to be on the other side.
Collect all the terms with r on the left of = and everything else on the right. So we need to move the 12 to the other side.
To remove 12 from the left we do the following
Any number multiplied by 1 does not change its value. We need r on its own. So we change the 4 into 1
Divide both sides by
This is the same as
For add, move the term to the other side of the = and change the sign to subtract.
For subtract, move the term to the other side of the = and change the sign to add.
For multiply, move the term to the other side and divide by it.
For divide, move the term to the other side of the = and multiply by it.
Hope this helps in solving other question.