Solving One-Step Equations • Topic 1 of 3

Solving Addition & Subtraction Equations

What is an Equation?

An equation is a mathematical sentence that shows two expressions are equal. It has an equals sign (=).

What does "Solving" mean?

Solving means finding the value of the variable that makes the equation true.

Inverse Operations:

Operation	Inverse Operation
Addition (+)	Subtraction (-)
Subtraction (-)	Addition (+)
Multiplication (×)	Division (÷)
Division (÷)	Multiplication (×)

Golden Rule: Whatever you do to one side of the equation, you MUST do to the other side!

SOLVING ADDITION EQUATION: x + 8 = 15

    x + 8 = 15
         │
         ▼
    Isolate x by subtracting 8 from BOTH sides
         │
         ▼
    x + 8 - 8 = 15 - 8
         │
         ▼
    x = 7
    
    Check: 7 + 8 = 15 ✓


SOLVING SUBTRACTION EQUATION: y - 4 = 10

    y - 4 = 10
         │
         ▼
    Isolate y by adding 4 to BOTH sides
         │
         ▼
    y - 4 + 4 = 10 + 4
         │
         ▼
    y = 14
    
    Check: 14 - 4 = 10 ✓


BALANCE SCALE MODEL:

    Equation: x + 3 = 8
    
    ┌─────────────────────────────────┐
    │                                 │
    │   x + 3         8              │
    │   ┌─┐┌─┐        ┌─┐            │
    │   │ ││ │        │ │            │
    │   │ ││ │        │ │            │
    │   └─┘└─┘        └─┘            │
    │   ════════════════════         │
    │                                 │
    └─────────────────────────────────┘
    
    Remove 3 from both sides:
    
    ┌─────────────────────────────────┐
    │                                 │
    │   x             5              │
    │   ┌─┐          ┌─┐             │
    │   │ │          │ │             │
    │   │ │          │ │             │
    │   └─┘          └─┘             │
    │   ════════════════════         │
    │                                 │
    └─────────────────────────────────┘
    
    So x = 5

Solved Examples

Worked Example

Solve: x + 8 = 15

Solution

To isolate x, subtract 8 from both sides
x + 8 - 8 = 15 - 8
x = 7
Answer: x = 7

Worked Example

Solve: y - 4 = 10

Solution

To isolate y, add 4 to both sides
y - 4 + 4 = 10 + 4
y = 14
Answer: y = 14

Worked Example

Solve: z + 12 = 25

Solution

Subtract 12 from both sides
z + 12 - 12 = 25 - 12
z = 13
Answer: z = 13

Worked Example

Solve: a - 7 = 18

Solution

Add 7 to both sides
a - 7 + 7 = 18 + 7
a = 25
Answer: a = 25

Key Points

Isolate variable by using inverse operations
Addition → subtract from both sides
Subtraction → add to both sides
Check answer by substituting back

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.To solve $x+5=12$, you:

Explanation: Subtract $5$.

Q2.To solve $x-3=8$, you:

Explanation: Add $3$.

Q3.The solution of $x+4=9$ is:

Explanation: $x=5$.

Q4.Addition and subtraction are ___ operations.

Explanation: Inverse.

Practice more MCQs → 📝 Assignment · 35 marks