### Notation for solving equations

I just found this via Math Teachers at Play...

Carolin's Notation for Solving Equations

Carolin is a student from Germany. I just wanted to note that that is exactly how I was taught (in Finland) to note what is done to each side of the equation, and I really like the notation. I don't know if it's used in all Europe...

Basically, you note in "the right side margin" what you're going to do to both sides of the equation in your next step. The "margin" is made by writing a vertical line to the far right of your actual equation solving process.

I just wanted to pass this on in case some of you who are teaching how to solve equations find it useful with students.

Carolin's Notation for Solving Equations

Carolin is a student from Germany. I just wanted to note that that is exactly how I was taught (in Finland) to note what is done to each side of the equation, and I really like the notation. I don't know if it's used in all Europe...

Basically, you note in "the right side margin" what you're going to do to both sides of the equation in your next step. The "margin" is made by writing a vertical line to the far right of your actual equation solving process.

```
6x - 5 = 2x | -2x
4x - 5 = 0 | +5
4x = 5 | ÷4
x = 5/4
```

I just wanted to pass this on in case some of you who are teaching how to solve equations find it useful with students.

## Comments

The main reason of this short note to you is to tell you that the "European" notation for solving equations was (and perhaps still is) used in Czechoslovakia when I was going to school there in the fifties. It is practical and makes a lot of sense, but I almost forgot it. Thanks for reminding me. I will use it when I teach my granddaughters the art of solving equations.

Cheers

Paula Tyroler

I used to tell students to memorize this strategy for solving linear equations in one variable:

a) Distribute (a rule for eliminating brackets)

b) Combine similar terms (reduces linear equations to two terms on each side)

c) Add the opposite (of the smaller variable term, of the smaller constant term) to both sides (reduces a linear equation to two non-zero terms, total)

d) Multiply both sides by the reciprocal of the numerical coefficient of the variable term (solution: x=5, or whatever).

They were to indicate, with curved arrows from line to line (as your student uses "|") to show what they had done (e.g., +(-2x+3)).