Learning Objectives
You should be able to:
- Explain what substitution means.
- Replace variables with given numbers.
- Evaluate simple algebraic expressions.
- Substitute more than one value into an expression.
- Avoid common substitution mistakes.
Introduction
This lesson develops Substitution from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
🎬 Replace the letter with its value
For x = 4, substitute first, then calculate.
🤔 Think About This...
Imagine that one bottle of juice costs x dollars.
The cost of three bottles can be written as:
Now suppose the shop tells you that one bottle costs $4.
This means:
We replace x with 4:
You have just used substitution.
📖 What is Substitution?
Substitution means replacing a variable with its given value.
For example, if:
Find the value of:
Replace x with 6:
🪜 The StudyNest Substitution Shortcut
- Substitute: Replace every letter with its given value.
- Simplify: Rewrite the expression as a calculation.
- Solve: Work out the final answer.
✖️ Remember Hidden Multiplication
When a number is written next to a variable, multiplication is understood.
So if:
Then:
📝 Worked Examples
Example 1
If x = 9, find:
Step 1: Substitute
Step 2: Solve
Example 2
If a = 7, find:
Step 1: Substitute
Step 2: Solve
Example 3
If m = 5, find:
Step 1: Substitute
Step 2: Simplify
Step 3: Solve
Example 4
If x = 6 and y = 3, find:
Step 1: Substitute both values
Step 2: Solve
Example 5
If a = 4 and b = 2, find:
Step 1: Substitute
Step 2: Simplify
Step 3: Solve
➖ Substituting Negative Numbers
Negative numbers should be placed inside brackets when substituted.
If:
Find:
Substitute using brackets:
🌍 Algebra Around Us
🍞 Bread
If one loaf costs b dollars and b = 2, then five loaves cost:
🚌 Kombi Fare
If one trip costs k dollars and k = 1.50, then four trips cost:
📱 Airtime
If x = 5, then:
📚 Exercise Books
If one book costs p dollars and p = 3, then six books cost:
⚠ Common Mistakes
If x = 4, then 5x = 5 × 4 = 20, not 54.
If x = 3, then x + 2x becomes 3 + 2(3).
Use brackets when substituting negative values.
Practice Questions
Given that x = 8, find:
- x + 2
- 3x
- 5x − 4
- x ÷ 2
- 4x + 6
Given that a = 5 and b = 2, find:
- a + b
- 3a
- 2a + b
- 4a − b
- ab
✅ Show Answers
- 10
- 24
- 36
- 4
- 38
- 7
- 15
- 12
- 18
- 10
🧠 Did You Know?
⭐ What You Can Do Now
- ✅ I know what substitution means.
- ✅ I can replace variables with numbers.
- ✅ I understand that 5x means 5 × x.
- ✅ I can substitute more than one value.
- ✅ I can substitute negative values using brackets.
🎉 Well Done!
You can now replace letters with numbers and calculate the value of algebraic expressions.
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
📈 Your Progress
Lesson 5 of 22
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Understand the meaning of each idea before selecting a method.
- Use definitions, properties and notation consistently.
- Show working and check that the final result is sensible.