**Algebraic expression is a meaningful combination of numbers and letters.**

**Difference between an algebraic equation and an algebraic expression.**

*An algebraic equation has an equal sign while an algebraic expression does not have an equal sign.*

**Note**:

An algebraic expression cannot be simplified any further.

**Steps followed in forming algebraic expressions are:**

#### Example 1

Wanja’s age is four times the age of Atieno.

Calculate the sum of their ages in five years time.

#### Solution

Let the age of the younger person (Atieno) be x

Therefore Wanja’s age is 4x

After 5 years:

Wanja’s age will be 4x + 5

Atieno’s age will be x + 5

Sum of their ages = x + 5 + 4x + 5

Collect the like terms: x + 4x + 5 + 5

= 5x + 10 years

= 5(x + 2) years

#### Example 2

A group of pupils went for a trip in x vehicles.

If y vehicles carried 20 pupils each, find the number of pupils who went for the trip if the remaining vehicles carried 15 pupils each.

#### Solution

Number of vehicles = **x**

Total number of pupils carried by y vehicles

= **20** multiplied by **y**

= **20y** pupils

Remaining vehicles

= (x – y)

Total number of pupils carried by the remaining vehicles

= 15 multiplied by (x – y)

= 15(x – y)

Open the brackets

15x – 15y pupils

Total number of pupils who went for the trip

= 20y + 15x – 15y

collect the like terms together

= 20 y( – 15y ) + 15x

= 5y + 15x

= 15x + 5y

#### Example 3

The length of a rectangle is thrice the width. If the perimeter is 48cm, what is the width?

#### Solution

Look at this,

Lets have x to represent both the length and the width.

Relate length to width ,so let y stand for width and 3y for length. see the image below.

Perimeter = length + width + length + width

=2(l+w)

Substitute length with 3y

And width with y

48cm = 3y + y + 3y + y

48cm = 8y (divide both sides by 8)

y=6cm

Therefore the width of the rectangle = 6cm

And the length = 3(6)= 18cm

**Example 4**

Solution

Let the number be k

Multiply it by 3 to get 3k

Add 6 to the product = 3k+6

The result is 21, so the equation is:

3k + 6 = 21

Solve the equation by

Subtracting 6 from both sides of the equation

3k+6-6=21-6

3k=21-6

3k = 15 (dividing both sides by 3)

K/3=15/3

Therefore:

K=5

The Number is 5

- FAExp.1 by elimu used under CC_BY
- FAExp.2 by elimu used under CC_BY-SA
- FAExp.3 by elimu used under CC_BY
- FAExp.4 by elimu used under CC_BY
- wanja by elimu used under CC_BY
- school_buses by elimu used under CC_BY
- FAExp.5 by elimu used under CC_BY
- FAExp.6 by elimu used under CC_BY
- FAExp.7 by elimu used under CC_BY

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