Solving Linear Equations
Use algebraic methods to solve linear equations in one variable, including equations that require rearrangement, expanding brackets, and collecting terms on both sides; solve equations with rational number 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
The lesson
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. Still divide (or multiply) both sides by whatever number is stuck to x, negative or not.
Whatever operation you use, apply it to both sides, until x stands alone.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.