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Solving Equations Step-by-Step | Master One-Step & Two-Step Equations Easily
Year 7 & 8 • Algebra
Lesson: Solving Equations
Learn how to solve one-step and two-step equations using the balancing method and inverse operations – with clear explanations, worked examples, and practice questions for Year 7 & 8 students.
Lesson Objectives
- Understand what an equation is.
- Use inverse operations to “undo” additions, subtractions, multiplications and divisions.
- Solve one-step and two-step equations using the balancing method.
- Check your solutions by substitution.
1. What Is an Equation?
An equation is a mathematical statement that shows two things are equal, using an equals sign =.
It usually contains a number and a variable (letter) that we want to find.
Examples of equations:
x + 5 = 12
3y = 21
2a − 7 = 9
x + 5 = 12
3y = 21
2a − 7 = 9
Here, we want to find the value of x, y or a that makes the equation true.
2. Balancing Method and Inverse Operations
To solve an equation, we keep both sides of the equation balanced.
We use inverse operations (doing the opposite) to “undo” what has been done to the variable.
Inverse operations:
Addition ↔ Subtraction
Multiplication ↔ Division
Addition ↔ Subtraction
Multiplication ↔ Division
Rule:
Whatever you do to one side of the equation,
you must do to the other side as well.
Whatever you do to one side of the equation,
you must do to the other side as well.
3. Solving One-Step Equations
A one-step equation can be solved using just one inverse operation.
Example 1:
x + 7 = 15
Use inverse of +7 → subtract 7 from both sides:
x + 7 − 7 = 15 − 7
x = 8
x + 7 = 15
Use inverse of +7 → subtract 7 from both sides:
x + 7 − 7 = 15 − 7
x = 8
Example 2:
5y = 35
Use inverse of ×5 → divide both sides by 5:
5y ÷ 5 = 35 ÷ 5
y = 7
4. Solving Two-Step Equations
A two-step equation needs two inverse operations.
Usually we undo addition/subtraction first, then multiplication/division.
Example:
3x + 4 = 19
3x + 4 = 19
Step 1: Undo +4 by subtracting 4 from both sides:
3x + 4 − 4 = 19 − 4
3x = 15
Step 2: Undo ×3 by dividing both sides by 3:
3x ÷ 3 = 15 ÷ 3
x = 5
5. Checking Your Solution
You can check your answer by substituting the value back into the original equation.
For 3x + 4 = 19, we found x = 5.
Substitute x = 5:
3(5) + 4 = 15 + 4 = 19 ✔
Since both sides are equal, our solution is correct.
Substitute x = 5:
3(5) + 4 = 15 + 4 = 19 ✔
Since both sides are equal, our solution is correct.
Practice Questions
A. One-Step Equations
Solve each equation:
- x + 9 = 14
- y − 5 = 11
- 4n = 28
- p ÷ 3 = 6
B. Two-Step Equations
Solve each equation:
- 2x + 3 = 15
- 5y − 4 = 26
- 3a + 7 = 25
- 4n − 5 = 19
C. Mixed Questions
- 7 + x = 20
- 3m − 2 = 16
- k ÷ 4 + 3 = 8
- 2(p − 1) = 10
D. Word Problems
-
A number increased by 6 is 19.
Write an equation and find the number. -
Three times a number minus 4 is 17.
Write an equation and solve it.
✅ Show Answer Key
A. One-Step Equations
- x + 9 = 14 → x = 14 − 9 = 5
- y − 5 = 11 → y = 11 + 5 = 16
- 4n = 28 → n = 28 ÷ 4 = 7
- p ÷ 3 = 6 → p = 6 × 3 = 18
B. Two-Step Equations
- 2x + 3 = 15
2x = 15 − 3 = 12 → x = 12 ÷ 2 = 6 - 5y − 4 = 26
5y = 26 + 4 = 30 → y = 30 ÷ 5 = 6 - 3a + 7 = 25
3a = 25 − 7 = 18 → a = 18 ÷ 3 = 6 - 4n − 5 = 19
4n = 19 + 5 = 24 → n = 24 ÷ 4 = 6
C. Mixed Questions
- 7 + x = 20 → x = 20 − 7 = 13
- 3m − 2 = 16 → 3m = 18 → m = 18 ÷ 3 = 6
- k ÷ 4 + 3 = 8 → k ÷ 4 = 5 → k = 5 × 4 = 20
- 2(p − 1) = 10 → p − 1 = 10 ÷ 2 = 5 → p = 5 + 1 = 6
D. Word Problems
-
“A number increased by 6 is 19”
Equation: x + 6 = 19 → x = 19 − 6 = 13
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