1. Algebra

2. What is algebra?
Used in everyday life e.g. splitting a bill in a restaurant.
Cost (£) = Total
Number of people.
C = T P
In science, e.g. finding the speed that an object is travelling.
Speed = Distance
Time

3. Simplifying equations
Simplify these equations;
Example: a + a + a simplified is 3a. c +c – f simplified is 2c – f
1. h + h + h + h = x f = b + b + b =
4. g + g – g = d + f + d + f = a + b + a + 2b + a

4. Simplifying equations
Simplify these equations;
Example: a + a + a simplified is 3a. c +c – f simplified is 2c – f
1. h + h + h + h = 4h x f = 3f b + b + b = 3b
4. g + g – g = g d + f + d + f = 2d +2f
6. a + b + a + 2b + a =3a+3b

5. Solving simple formulae
Example: Find the value of p
3p + 55 = 82
Move the numbers to one side of the equals sign and letters to the other.
When you change the side, you change the sign.
3p = 82 – 55
3p = 27
p = 27/3
p = 9
Have a go!
3z – 12 = r + 14 = n + 1 = 1001
6q – 30 = a – 12 = 72

6. Solving simple formulae
Example: Find the value of p
3p + 55 = 82
Move the numbers to one side of the equals sign and letters to the other.
When you change the side, you change the sign.
3p = 82 – 55
3p = 27
p = 27/3
p = 9
Have a go!
3z – 12 = 168 z = 60 3r + 14 = 47 r = 11 4n + 1 = 1001 n =250
6q – 30 = 42 q = a – 12 = 72 a =7

7. Substituting with values.
If a = 5, b = 3 and c = 1, solve these equations;
Example: 3a + b = (3 x 5) + 3 = 18
Don’t forget BODMAS, which is Brackets, order, division, multiplication, addition, subtraction.
3a + b = b – c = a + 3b =
4. 2b – 2c = a – b – c = b + 7c =
7. 4a ÷ 2 = c x 10 = b + 3c + 8a

8. Substituting with values.
If a = 5, b = 3 and c = 1, solve these equations;
Example: 3a + b = (3 x 5) + 3 = 18
Don’t forget BODMAS, which is Brackets, order, division, multiplication, addition, subtraction.
2b – c = 5 a + 3b = 14
2b – 2c = 4 a – b – c = 1 5b + 7c = 22
4a ÷ 2 = c x 10 = b + 3c + 8a = 61

9. Combining like terms:
Example: 22 – 4T = T group the like terms together
22-10 = 8T + 4T (change the side, change the sign)
12 = 12T Now, get T on its own.
12/12 = T
1 = T
5U + 7 = 56 – 2U 
30 + 2V = 15 +7V
6W – 20 = 15 + W
62 + 7X = 152 – 8X
7Y + 12 – 5Y = 42
4Z + 27 = Z

10. Combining like terms:
Example: 22 – 4T = T group the like terms together
22-10 = 8T + 4T (change the side, change the sign)
12 = 12T Now, get T on its own.
12/12 = T
1 = T
5U + 7 = 56 – 2U  U = 7
30 + 2V = 15 +7V V = 3
6W – 20 = 15 + W W = 7
62 + 7X = 152 – 8X X = 6
7Y + 12 – 5Y = 42 Y = 15
4Z + 27 = Z Z = 1.5

11. Solving equations involving brackets
5( x -4) = 30 First, expand the bracket
5x – 20 = 30 Now, it’s very much like our previous examples.
5x =
5x = 50
x = 10
Try these:
2(3x – 4) = 28 2(a – 3) = 15 3(t - 11) = 2(t + 8)

12. Solving equations involving brackets
5( x -4) = 30 First, expand the bracket
5x – 20 = 30 Now, it’s very much like our previous examples.
5x =
5x = 50
x = 10
Try these:
2(3x – 4) = 28 x = 6 2(a – 3) = 15 a = 10.5
3(t - 11) = 2(t + 8) T = 49

13. Any questions?