# How do you solve for r in #4(r+3)=t#?

##### 2 Answers

r=t-12/4

#### Explanation:

4[r+3]=t

4r+12=t

4r=t-12

r=t-12/4

#### Explanation:

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

So

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Given:

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.

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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

Subtract

But

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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

But

But

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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.