Math101 · Independent Ontario learning library
Math101Linear Equation
Solve a linear equation by preserving equality while undoing the operations around the variable.
A linear equation states that two expressions are equal and contains variables only to the first power.
Equality is a balance
An equation such as
$$
3x-7=11
$$
is balanced for one particular value of $x$. Solving means finding that value without breaking the equality.
Inverse operations
| Operation present | Operation that undoes it |
|---|---|
| add $a$ | subtract $a$ |
| subtract $a$ | add $a$ |
| multiply by $a$ | divide by $a$ |
| divide by $a$ | multiply by $a$ |
A two-step equation
Why order matters
In $3x-7$, the value $x$ is multiplied by $3$ and then $7$ is subtracted. Solving reverses the process: undo subtraction first, then multiplication. It is like removing an outer layer before an inner layer.
Common mistakes
A solving checklist
- Simplify each side.
- Collect variable terms on one side.
- Collect constants on the other.
- Divide by the remaining coefficient.
- Check in the original equation.
