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+---- Thread: Algebra Basics — Understanding the Language of Maths (/showthread.php?tid=60)
Algebra Basics — Understanding the Language of Maths - Leejohnston - 11-13-2025
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.