Solving linear equations
Use algebraic methods to solve linear equations in one variable, including rearranging, expanding brackets, collecting terms on both sides, and working with rational coefficients.
What a learner can do afterwards
- Solve one-step and two-step linear equations in one variable
- Solve equations requiring expansion of brackets and collection of like terms
- Solve equations with the unknown on both sides and with fractional or negative coefficients
1 · Read
An equation is like a balance. Both sides always stay equal. Your job is to get x alone on one side, using inverse operations to undo whatever has been done to it.
To solve 3(x + 2) = 21, expand the bracket first: 3x + 6 = 21. Subtract 6 from both sides: 3x = 15. Divide by 3: x = 5.
When x is on both sides, like 5x - 4 = 2x + 8, move the x terms together first. Subtract 2x from both sides: 3x - 4 = 8. Add 4: 3x = 12. Divide by 3: x = 4.
A negative or fractional coefficient does not change the plan. Divide or multiply both sides by the coefficient of x, whether it is negative or fractional.
Whatever operation you use, apply it to both sides, until x stands alone.
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2 · Watch
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Where it sits
Where this leads
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