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Lesson Algebra

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Questions:

1. 2x + x + 5x =

2. 3a + 4b + 6a – 10b =

3. 4x – 9y +7x +3y =

4. 4m + 3n -2 -5n – 6 +3m =

5. -10x + 3y – 5x – 10y =

6. 13a – 15b +12c – 8a +3b -10c =

AlgebraAlgebra is a system in maths where we use letters to represent unknown values. It

could as easily be a question mark or empty box.So if I say Emma and Sean’s age added together is 62 we could write this as:

x + y = 62

There are a number of rules to algebra which must be learnt so that they become second nature.

Rule 1 You can only add like terms. Much like you can’t add apples to oranges, you can only add terms that are the same

x + x + 2x = 4x

n + n + n = 3n

x + 5 + 2x + 8 = 3x + 13

x + 2y + 3x + 4y = 4x + 6y

You can only add x terms together. You can only add y terms together. You can only add numbers together and never the twain shall meet.

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Questions:

a) a x a

b) a x a x a

c) 5 x a x a

d) 3p x p

e) q x 4q

f) 3r x 3r

g) 5c x 6c

h) t x 2t

i) e x e2

j) 3f x 4f2

k) x2 x x3

l) 5p x -3p

m) 2q2 x 7q

n) -2a x 7q

o) -2a x 5a2

p) 2d3 x 5d

q) (6h)2

r) (2a)3

s) (3x)2

Rule 2When you are multiplying like terms you add the indices (or powers). If there is no power or indice indicated it is assumed that the value is 1.

x x x = x2 x x x x x = x3

M 2 x N 3 x M 6 x N 4 = M (2+6) x N (3+4) = M 8 x N 7

3a x 4b = 12ab5x x -6y = -30xy2a x 2b x 4a x 6b = (2 x 2 x 4 x 6) x a2 x b2 = 96a2b2

HINT: Do the numbers first, then do the letters, one letter at a time.

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Example:

Rule 3When dividing like terms SUBTRACT the powers and put the answer where the biggest power was

How?x4 = x x x x x x x x2 = x x xx4 = x x x x x x x = x2

x2 = x x x

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Questions:

a) 2(3x-y)b) 2n(n-5)c) -4(2n+1)d) 3(4a-3b)e) 6(x+9y)f) -3(5a-5b)g) -2(-5x+3y)h) 3x(2x-8y)i) 4a(3-6a)j) 2m(5m+2m)k) 3L(2a+5b+6c)l) -3b(2a-8b+12c)

Rule 4

Multiplying out Brackets1)4 ( x + 3y )

Multiply each term by the number outside the bracket.Sometimes called multiplying out the brackets.4 x x = 4x4 x 3y = 12ySo,

4 ( x + 3y ) = 4x + 12y

2) -4 ( 2a -3b + 4c ) = -8a +12b -16c

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Simplify:

Simplify and Collect terms

Multiply out your brackets and collect like terms

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Solve:

7. Find the values of the following fomulae based on the information given.

a=2 b=0 c=-3

Substituting into formulas

Formulas for common and uncommon measurements are usually presented in a form of algebra. Where this is the case, the letters are used to represent a term. The task is then to identify which value goes into which term and solve.

Example: If a = 2 b = -3 c = 1

Work out the value of 2a – 3b + 4c = 2(2) – 3(-3) +4(1) = 4 + 9 + 4 = 17

In the formula v = ut + at where u is the initial speed v is the final speed, a is the acceleration and t is the time what is the final speed if the initial speed is 6 m/s, the car accelerates at 9 m/s2 and the time is 2 seconds?Substitute the appropriate values into the formula

V = 6+(9)(2) = 6+18 = -12

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Solve:

(a) 2x – 1 = x + 5

(b) 8x + 7 = 3x – 2

(c) 5x – 6 = 3x + 8

(d) x – 7 = 4X + 11

(e) 2x – 5 = 4x – 9

(f) 6y + 1 = 7y – 3

(g) 3w + 4 = 39 – 2w

(h) 12 + 6v = 2v + 30

(i) 6z – 9t = 2t – 4

Pulling it all together

When there are several numbers to take across, take them one at a time, starting with the one furthest away from the letter you are looking for.

Ideally if you have xs on both sides and numbers on both sides you want to get the xs all on one side and the numbers on the other.

Example 5Solve 2x – 6 = 12Ans: 2x = 12 + 6 2x = 18

x = 9

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Solve:

(a) x-6=9

(b) x+3=12

(c) x-8=15

(d) x=7=12

(e) 8=x+3

(f) 17=x-4

(g) x+10=-8

(h) x-12=-20

Setting up and solving simple equations

There are a number of main rules to manipulating formulas.The main one is that if a number crosses the equals sign it does the opposite of what it was doing before.For example an added number becomes a subtracted number when moved across & vice versa.

1) Solve x– 5 = 3Ans: x = 3+5

x = 8

2) Solve x + 6 = -7Ans: x = -7 - 6

x = -13

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Solve:

(a) 3x = 12

(b) 4x = -20

(c) 8x = 10

(d) 12 = 6x

(e) 18 = 9x

(f) -24 = 4x

(g) = 9

(h) = 7

Setting up and solving simple equations (multiplying and dividing

For example a multiplied number becomes a divided number when moved across & vice versa.

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Harder Examples

(a) 4(3x –1) = 6(x+4)

(b) 3(x + 2) = 2(x + 1)

(c) 2(2x – 3) – (3x – 7) = 6

(d) 4(7x– 1) = 9(x +8)

e) 5(2x + 7) = 2(x – 2) +1

f) 3(4x + 5) – 2 (2x – 5) = 6(5x +1) + 2