Solving linear equations is one of the most important skills in algebra. Once you understand the step-by-step process, you can solve all sorts of math problems with confidence.
In this blog post, you’ll learn:
What a linear equation is
The rules of solving them
Easy step-by-step examples
Common mistakes to avoid
Let’s get started!
What Is a Linear Equation?
A linear equation is an equation that forms a straight line when graphed. It usually looks like:
ax + b = c
Where:
x is the variable (unknown)
a, b, and c are numbers
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The Goal: Find the value of x
Basic Steps to Solve Linear Equations
Let’s walk through the core steps for solving a simple equation.
Example 1:
2x + 4 = 10
Step 1: Subtract or Add to Get Variable Alone
We want to move 4 to the other side by subtracting it:
2x + 4 − 4 = 10 − 4
2x = 6
Step 2: Divide or Multiply to Isolate the Variable
Now divide both sides by 2:
2x ÷ 2 = 6 ÷ 2
x = 3
Answer: x = 3
More Examples (With Explanations)
Example 2:
3x − 7 = 11
Step 1: Add 7 to both sides
3x = 18
Step 2: Divide both sides by 3
x = 6
Answer: x = 6
Example 3:
5 − 2x = 1
Step 1: Subtract 5 from both sides
−2x = −4
Step 2: Divide both sides by −2
x = 2
Answer: x = 2
Key Rules to Always Remember:
- Whatever you do to one side, do to the other.
- Use inverse operations (opposite of + is −, opposite of × is ÷).
- Keep your work neat to avoid mistakes.
- Always check your answer by plugging it back in.
Common Mistakes to Avoid
❌ Forgetting to change the sign when moving terms
❌ Not dividing correctly
❌ Skipping steps or doing mental math too quickly
❌ Misplacing negative signs
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Can You Try It Yourself!
Problem 1:
4x + 3 = 19
Step 1: Subtract 3 → 4x = 16
Step 2: Divide by 4 → x = 4
Answer: x = 4
Problem 2:
2x − 5 = 9
Step 1: Add 5 → 2x = 14
Step 2: Divide by 2 → x = 7
Answer: x = 7
Bonus: What If the Variable Is on Both Sides as shown below?
2x + 3 = x + 9
Step 1: Get all variables on one side
2x − x = 9 − 3
x = 6
Answer: x = 6
Summary: Step-by-Step Checklist
Step 1: Move numbers (add/subtract)
Step 2: Move variables (if needed)
Step 3: Isolate the variable
Step 4: Simplify and solve Step 5: Check your answer!