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+---- Thread: Equation Solving Basics — Step-by-Step for Beginners (/showthread.php?tid=63)
Equation Solving Basics — Step-by-Step for Beginners - Leejohnston - 11-13-2025
Equation Solving Basics — Step-by-Step for Beginners
Solving equations is about finding the value of the unknown number (usually x).
The goal is simple:
Get x by itself.
Here is the beginner-friendly guide.
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1. What Is an Equation?
An equation has:
• two sides
• an equals sign
• an unknown (x, y, etc.)
Examples:
• x + 5 = 12
• 4x = 20
• 3x – 2 = 13
An equation is true only when x has the correct value.
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2. Opposite Operations
To solve equations, you “undo” what is happening.
Use the opposite operation:
Add ↔ Subtract
× ↔ ÷
Examples:
• If the equation adds 6 → subtract 6
• If it multiplies by 4 → divide by 4
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3. Solving One-Step Equations
Example 1:
x + 7 = 15
→ subtract 7
x = 8
Example 2:
4x = 28
→ divide by 4
x = 7
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4. Solving Two-Step Equations
Example:
3x + 5 = 20
Step 1: subtract 5
3x = 15
Step 2: divide by 3
x = 5
Another example:
2x – 4 = 10
Add 4 → 2x = 14
Divide by 2 → x = 7
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5. Solving Equations with Brackets
Expand the bracket first.
Example:
2(x + 3) = 14
→ 2x + 6 = 14
→ subtract 6 → 2x = 8
→ divide 2 → x = 4
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6. Solving Equations with Fractions
Example:
x/3 = 7
Multiply both sides by 3 → x = 21
Example:
(x + 1)/5 = 4
Multiply both sides by 5 → x + 1 = 20
Then subtract 1 → x = 19
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7. Checking Your Answer
Always substitute back in:
Example:
Equation: 3x + 1 = 10
Your answer: x = 3
Check: 3(3) + 1 = 10 ✔
Checking helps catch mistakes — especially on exams.
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8. Common GCSE Mistakes
❌ Forgetting to do the same thing to both sides
❌ Expanding brackets incorrectly
❌ Adding instead of subtracting
❌ Rushing negative numbers
❌ Not checking the answer
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Summary
To solve equations:
• Isolate x
• Use opposite operations
• Work step-by-step
• Expand brackets if needed
• Check your answer
Master these basics and all algebra becomes easier — including GCSE problem-solving.