## Algebra: Solving Simple Equations Involving Addition and Subtraction

### Forming Simple Equations with One Unknown

Consider the following:

#### Practice Example 1:

We can form a simple equation to represent the total number of apples as:
4 + 5 = b
which can also be written as:
b = 4 + 5

#### Practice Example 2:

The number of boys in a school is n. The number of girls in the same school is 120. If the total number of student in the school is 330, form a simple equation that can be used to find the value of n.
n + 120 = 330
which can also be written as:

n = 330 - 120
Note
When we take the + 120 to the other side of the equation, the sign changes to minus (-) becoming - 120. The + and − signs change to the other when moved to either side of the equation.

#### Practice Example 3:

John had 14 mangoes and Newton had p mangoes. If the total number of mangoes they had was 45, form a simple equation that can be used to find the value of p.
Total number of mangoes was 45.
14 + p = 45.
p = 45 - 14

#### Practice Example 4:

The number of bags of beans harvest on Monday was 90. On Tuesday, y bags of beans were harvested. If the total number of bags harvested on Monday and Tuesday was 210, for a simple equation to show the number of bags harvested on Tuesday.
Monday: 90 bags
Tuesday: y bags
Total: 210 bags
90 + y = 210
y = 210 - 90

#### Practice Example 5:

A grade 5 pupil in your school bought k mangoes from the market. On his was home, he ate 4 mangoes. If he arrived home with 6 mangoes, form a simple equation to show how many mangoes he bought from the market
Total number of mangoes: k
Ate: 4 mangoes
Arrived with 6 mangoes
If we subtract the number of mangoes he ate, from the total number of mangoes, we get the number of mangoes he was left with.
k - 4 = 6.
The above equation can also be written as:
k = 6 + 4

### Solving Simple Equations Involving Addition and Subtraction

In the previous section, we learnt how to form simple equations. In this section, lets learn how to solve them.

#### Practice Example 6:

Solve: 40 + m = 90
The equation can be written as:
m = 90 - 40
m = 50

#### Practice Example 7:

Martha had 10 kg of beans and y kg of maize. Altogether, she had 25 kg of both maize and beans. How many kilograms of maize did Martha have?
→ 1. Lets form a simple equation:
10 kg + y kg = 25 kg
The above equation can also be written as:
y kg = 25 kg - 10 kg

→ 2. Lets solve the simple equation above:
y kg = 25 kg - 10 kg
y kg = 15 kg

#### Practice Example 8:

Solve: d - 4 = 9
The equation can be written as:
d = 9 + 4
d = 13

#### Practice Example 9:

Solve: f - 419 = 210
The equation can be written as:
f = 210 + 419
f = 629

Solve: 20 - t = 12
→ Step 1:

→ Step 2:

The above equation can be written as:
t + 12 = 20
t = 20 - 12
t = 8