Algebra · StudentHub Lesson
Linear Equations
Learn to solve one-variable linear equations using inverse operations to isolate the unknown.
What you will learn
- Understand what a linear equation represents
- Use inverse operations to isolate a variable
- Solve equations with variables on one or both sides
- Check solutions by substitution
- Translate word problems into equations
Watch the lesson
Algebra: Linear equations 1 · Khan Academy
Watch on YouTubeTopic notes
Main Idea
A linear equation shows two expressions are equal and contains a variable raised to the power 1. Solving means finding the value that makes the equation true.
Key Concepts
- Equations must stay balanced: whatever you do to one side, do to the other
- Use inverse operations (opposite operations) to undo steps around the variable
- Work step by step: undo addition/subtraction first, then multiplication/division
Definitions
- Variable: an unknown quantity represented by a letter
- Coefficient: the number multiplying a variable
- Solution: the value of the variable that makes the equation true
Formulas
- General form: ax + b = c
- To solve: x = (c - b) / a
Examples
- 3x + 5 = 20 → 3x = 15 → x = 5
- 2(x - 1) = 8 → 2x - 2 = 8 → 2x = 10 → x = 5
Common Mistakes
- Forgetting to apply an operation to both sides
- Sign errors when moving terms across the equals sign
- Not distributing correctly through brackets
Key concepts
Important terms
- Variable
- A letter representing an unknown number.
- Coefficient
- The number multiplied by a variable.
- Solution
- The value that makes an equation true.
Worked examples
Problem
Solve 2x + 4 = 10
- 1. Subtract 4 from both sides
- 2. 2x = 6
- 3. Divide both sides by 2
- 4. x = 3
Answer: x = 3
Problem
Solve 5x - 3 = 2x + 9
- 1. Subtract 2x from both sides
- 2. 3x - 3 = 9
- 3. Add 3 to both sides
- 4. 3x = 12
- 5. Divide by 3
- 6. x = 4
Answer: x = 4
Quick revision
- Keep both sides balanced
- Undo addition/subtraction first
- Then undo multiplication/division
- Combine like terms before solving
- Always check your answer by substituting back
- Watch signs when moving terms
Check your understanding
Question 1 · Multiple choice
Solve for x: x + 7 = 12
Question 2 · Multiple choice
Solve for x: 3x = 21
Question 3 · Short answer
Solve 4x - 5 = 11
Question 4 · Short answer
Solve 2(x + 3) = 16
Question 5 · True or false
In an equation, you must apply the same operation to both sides to keep it balanced.
Done with Linear Equations?
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