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- Solving linear equations
Solving linear equations
An equation is a balance. Keep both sides equal and peel away everything around x until it is on its own.
Keep it balanced
Whatever you do to one side, do to the other side.
Undo operations in reverse order: first undo + and −, then undo × and ÷.
3x + 5 = 20 → 3x = 15 → x = 5
Undo operations in reverse order: first undo + and −, then undo × and ÷.
3x + 5 = 20 → 3x = 15 → x = 5
x on both sides
Move the x terms to the side with more x, so you avoid negatives.
5x − 7 = 2x + 8 → take 2x from both sides → 3x − 7 = 8
5x − 7 = 2x + 8 → take 2x from both sides → 3x − 7 = 8
Brackets and fractions
Expand brackets first. For a fraction, multiply both sides by the denominator.
x4 + 1 = 3 → x4 = 2 → x = 8
x4 + 1 = 3 → x4 = 2 → x = 8
Solve 5x − 7 = 2x + 8
- Take 2x from both sides: 3x − 7 = 8
- Add 7 to both sides: 3x = 15
- Divide both sides by 3: x = 5
- Check: 5 × 5 − 7 = 18 and 2 × 5 + 8 = 18. It balances.
Answer: x = 5
Do the same to both sides. Collect x on one side, numbers on the other, then divide. Always check by substituting back.
The interactive lesson includes the diagrams for this topic.
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