Equations with brackets

Some equations hide a bracket around part of the unknown:

3(x + 2) = 18

You can't undo this in one move — the x is trapped inside the bracket, multiplied by everything outside it. The trick is to deal with the bracket first. Expand it by multiplying the 3 across both terms inside:

3(x + 2) = 3x + 6

Now the equation has no bracket at all — it has become a plain two-step equation:

3x + 6 = 18

From here you solve it the way you already know. Undo the operations in reverse: first subtract the 6 that was added, then undo the multiplication by 3.

3x + 6 = 18 \;\Rightarrow\; 3x = 12 \;\Rightarrow\; x = 4

So the whole recipe is: expand the bracket, then solve the two-step equation. Once the bracket is gone, there is nothing new to learn.

See it solved

Step through the solution: first the bracket is expanded, then the two-step equation is solved one undo at a time.

See it explained

Sal Khan distributes across a bracket, then solves the equation that's left.