11-13-2025, 12:37 PM
Algebra Basics — Understanding the Language of Maths
Algebra is how we use symbols (usually letters) to represent numbers.
It lets us solve problems where the answer isn’t known yet.
If maths is a language, algebra is the grammar.
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1. What Is a Variable?
A variable is a letter that stands in for a number.
Examples:
• x = unknown number
• y = height, time, speed, etc.
• a, b, c = any values
Example expression:
x + 5
Means: “a number plus 5”
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2. Like Terms
You can only combine terms that have the same variable.
Examples:
• 3x + 7x = 10x
• 4a + a = 5a
Non-like terms:
• 3x + 2 (cannot combine)
• 5x + 5y (different letters)
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3. Simplifying Expressions
To simplify, collect all like terms.
Example:
3x + 4 + 2x + 1
→ (3x + 2x) + (4 + 1)
→ 5x + 5
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4. Using Brackets
Multiply everything inside the brackets.
Examples:
• 3(x + 2) = 3x + 6
• 2(a – 4) = 2a – 8
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5. Solving One-Step Equations
Goal: get the variable by itself.
Example:
x + 7 = 12
Subtract 7 from both sides:
x = 5
Example:
4x = 20
Divide both sides by 4:
x = 5
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6. Solving Two-Step Equations
Example:
2x + 3 = 11
Step 1: subtract 3
2x = 8
Step 2: divide by 2
x = 4
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7. Substitution
Replace the variable with a number.
Example:
If x = 3, find 2x + 4
→ 2(3) + 4 = 6 + 4 = 10
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8. Common Mistakes to Avoid
• Don’t combine unlike terms
• Remember to divide when undoing multiplication
• Always do the same operation to *both sides* of the equation
• Don’t forget bracket expansion
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Summary
Algebra becomes simple once you remember:
• Variables stand in for numbers
• Collect like terms
• Use opposite operations to solve equations
• Expand brackets carefully
• Substitute values correctly
Master these basics and you’ll be ready for higher-level algebra, GCSE exam questions, and real scientific maths.
Algebra is how we use symbols (usually letters) to represent numbers.
It lets us solve problems where the answer isn’t known yet.
If maths is a language, algebra is the grammar.
-----------------------------------------------------------------------
1. What Is a Variable?
A variable is a letter that stands in for a number.
Examples:
• x = unknown number
• y = height, time, speed, etc.
• a, b, c = any values
Example expression:
x + 5
Means: “a number plus 5”
-----------------------------------------------------------------------
2. Like Terms
You can only combine terms that have the same variable.
Examples:
• 3x + 7x = 10x
• 4a + a = 5a
Non-like terms:
• 3x + 2 (cannot combine)
• 5x + 5y (different letters)
-----------------------------------------------------------------------
3. Simplifying Expressions
To simplify, collect all like terms.
Example:
3x + 4 + 2x + 1
→ (3x + 2x) + (4 + 1)
→ 5x + 5
-----------------------------------------------------------------------
4. Using Brackets
Multiply everything inside the brackets.
Examples:
• 3(x + 2) = 3x + 6
• 2(a – 4) = 2a – 8
-----------------------------------------------------------------------
5. Solving One-Step Equations
Goal: get the variable by itself.
Example:
x + 7 = 12
Subtract 7 from both sides:
x = 5
Example:
4x = 20
Divide both sides by 4:
x = 5
-----------------------------------------------------------------------
6. Solving Two-Step Equations
Example:
2x + 3 = 11
Step 1: subtract 3
2x = 8
Step 2: divide by 2
x = 4
-----------------------------------------------------------------------
7. Substitution
Replace the variable with a number.
Example:
If x = 3, find 2x + 4
→ 2(3) + 4 = 6 + 4 = 10
-----------------------------------------------------------------------
8. Common Mistakes to Avoid
• Don’t combine unlike terms
• Remember to divide when undoing multiplication
• Always do the same operation to *both sides* of the equation
• Don’t forget bracket expansion
-----------------------------------------------------------------------
Summary
Algebra becomes simple once you remember:
• Variables stand in for numbers
• Collect like terms
• Use opposite operations to solve equations
• Expand brackets carefully
• Substitute values correctly
Master these basics and you’ll be ready for higher-level algebra, GCSE exam questions, and real scientific maths.