Linear Equations
Year 8 📊 Algebra Solve linear equations with unknowns on both sides.
⚖️ Solving Linear Equations
Linear equations have no powers higher than 1. Use inverse operations, working in reverse BODMAS order.
Example: Solve $5(2x - 3) = 25$ → expand: $10x - 15 = 25$ → add 15: $10x = 40$ → divide by 10: $x = 4$
↔️ Variables on Both Sides
Collect all variable terms on one side and number terms on the other.
- Expand any brackets.
- Add or subtract to get all $x$ terms on one side.
- Add or subtract to move all numbers to the other side.
- Divide by the coefficient of $x$.
Example: Solve $3x + 7 = x + 15$ → subtract $x$: $2x + 7 = 15$ → subtract 7: $2x = 8$ → $x = 4$
📐 Equations with Fractions
Multiply every term by the LCM of the denominators to clear all fractions.
Example: Solve $\frac{x+1}{3} = \frac{2x-1}{5}$ → multiply through by 15: $5(x+1) = 3(2x-1)$ → $5x+5 = 6x-3$ → $x = 8$
Always check your answer by substituting back into the original equation.
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Interactive Demonstration — Linear Equations
Solving ax + b = cx + d by graphing y = ax+b and y = cx+d
⚖️ Linear Equation Solver
Solve ax + b = cx + d for x.