| Brackets |
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Brackets
Brackets are used to group terms together.
If we want to remove brackets, then everything inside the bracket must be multiplied by the term on the outside.
3 (y + 2) = 3 x y + 3 x 2 = 3y + 6
Both y and the + 2 must be multiplied by 3.
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5 (y – 3) = 5 x y – 5 x 3
= 5y – 15
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Equations with Brackets
Example 1: Solve 5 (y – 3) = 20.
Remove the brackets:
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5y – 15 = 20 |
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5y = 20 + 15 |
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5y = 35 |
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y = 35 ÷ 5 |
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y = 7 |
| Example 2: Solve |
p + 4 = 5. |
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3 |
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Note: This line brackets p + 4 together. So we cannot (– 4) first.
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p + 4 = 5 x 3
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p + 4 = 15
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(– 4 from both sides) |
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p = 15 – 4
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p = 11 |
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Double Brackets
Example 1
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| (y + 3)(y + 2) = y(y + 2) + 3(y + 2) |
= y2 + 2y + 3y + 6 |
= y2 + 5y +6 |
Note: We multiply the second bracket by y and then by 3.
Example 2
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| (y + 5)(y – 2) = y(y – 2) + 5(y – 2) |
= y2 – 2y + 5y – 10 |
= y2 + 3y – 10 |
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Example 3
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(x – 3)(x – 4) = x(x – 4) – 3(x – 4)
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= x2 – 4x – 3x + 12 |
= x2 – 7x + 12 |
Note: This time we multiply by –3. This changes the signs in the second bracket.
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