**letters**are used to represent

**unknowns**and are used together with numbers.

**In algebra, always remember the following:**

n means 1 x n

2p means 2 x p

3y

^{2}means 3 x y

^{2}which is same as 3 x y x y

4a

^{2}d means 4 x a

^{2}x d

2(2a + 5b) = 2 x 2a + 2 x 5b = 4a + 10b

### Simplifying Algebraic Expressions

##### Example 1

Work out: 3(2a + 4b) - 2(a + 2b)
= (3 x 2a + 3 x 4b) - (2 x a + 2 x 2b)

= 6a + 12b - 2a + 4b

= 6a - 2a + 12b + 4b

= 4a + 16b

= 6a + 12b - 2a + 4b

*Putting like terms together*= 6a - 2a + 12b + 4b

= 4a + 16b

### Forming and Simplifying Algebraic Expressions

##### Example 2

Albert, Wilson and Charles shared some apples. Albert got 5 more apples than Charles who got twice as much as Wilson. How many apples did they get all together?*From the information above, we gather that:*

Wilson has

**a**apples. Hence:

Charles has

**(2 x a = 2a)**apples

Albert =

**(2a + 5)**apples

Hence

**= a + 2a + 2a + 5**

**= 5a + 5**

### Solving Algebraic Expressions

When solving a quadratic equation, you find the value of the unknown in the equation.

##### Example 3

Find the value of y in 3(y + 2) = 24*We start by opening the brackets:*

**3(y + 2)**is the same as

**(3 x y) + (3 x 2)**

**3y + 6 = 24**

3y = 24 - 6

3y = 18

3y = 24 - 6

3y = 18

*Divide both sides by 3:*

3y / 3 = 18 / 3

**y = 6**

### Forming and Solving Algebraic Expressions

Now that you have learnt how to solve algebraic expressions. Let's try solving real-life mathematical problems.In this section, you will come across words such as more than, greater than, less than, younger than, shorter than, twice as much and similar comparative words.

##### Example 4

Mwilu is 6 years older than Kyalo. If Kyalo is 12 years old, how old is Mwilu.*Let Mwilu's age be*

**b**:Then

**b = 6 years + Kyalo's age**.

**b = 6 + 12**

b = 18

b = 18

**Mwilu is 18 years age**

### Inequalities

Let us say an unknown number**p**is between 8 and 14 but is neither 8 or 14. Can you tell which number

**p**is likely to be?

**p**can be 9, 10, 11, 12, 13

From this, we can say that p is greater than 8 and less than 14.

This can be mathematically expressed as p > 8 and p < 14. This are called inequalities.

#### Simplifying Inequalities

##### Example 5

Simplify the following inequality: 3p - 2 > 19
3p - 2 > 19

*Collecting like terms together:***3p > 19 + 2**

3p > 21

3p > 21

*Divide both sides by 3:***3p / 3 > 21 / 3**

21 / 3 = 7

21 / 3 = 7

**p > 7**