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Before you dive in this section you will need to read the section on linear equations... Finished? Here we go.

 

We are going to solve horrible equations with brackets in! You will come across different types, here is one of them:

6(5x + 6) = 54

To do this, you need to multiply out the bracket. Surprisingly, this is done by multiplying everything inside the bracket by the number outside the bracket. This is what the result is:

6 X 5x + 6 X 6 = 54

(Please note that you don't multiply the RHS of the = sign by 6). Now that we have removed the brackets, we can see that this is a linear equation and therefore can be solved.

The next one you will encounter is of this form:

6(5x - 6) = 54

Do the same thing as last time, only make sure you multiply - 6 by 6, not 6 by 6. This gives:

6 X 5x - 6 X - 6 = 54. Once again, this can be solved as a linear equation.

Another type is:

-6(5x - 6) = 54

To solve this, multiply out the bracket (when you get to -6 X -6 change the two - signs to + signs) and solve the equation. Tedious!

BUT there IS one more type:

(6x + 4)(7x +9)

To solve this, do this:

(6x X 7x) + (6x X 9) + (4 X 7x) + (4 x 9)

which equals 42x+ 54x + 28x + 36

which equals 42x + 82x + 36.

Confused? What I have done is multiplied the 1st term in the 1st bracket by the 1st term in the 2nd bracket. To this I added the 1st term in the 1st bracket X 2nd term in 2nd bracket, the 2nd term in the 1st bracket X 1st term in 2nd bracket and the 2nd term in the 1st bracket X the 2nd term in the 2nd bracket, which gives the answer. Look again at the equation breakdown above and this will become clear.

 

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