# Equations

## Equating Equations

- Equations can be simple.
*eg., 3 + 2 = 5* - Equations can be simple and mysterious.
*eg., 3 + n = 5* - Equations can be complicated.
*eg., (4 + 2 × 5) ÷ (6 - 4)* - Equations can be complicated and mysterious.
*eg., (4n + 5y) + ( 3n - 2y)* - Equations can be very complicated.
*eg., (n² + 3n + 6y) + (3n² + n - 2y)*

### Simple Equations

A. Simple linear equations are just normal math addition, subtraction, multiplication and division problems.*eg., 3 + 3 = n or 3 + 3 = 6
*

B. Simple one variable linear equations where one of the inside numbers is missing require a bit more work.*eg., 8 + n = 10*

Method:

The math sentence has to be rearranged so it will make sense.

- The n needs to be all by itself on one side of the = sign.
- The 8 needs to move to the other side of the = sign.

+8 becomes -8 when it moves across the = sign*8 + n = 10**n = 10 - 8**n = 2*

### Complex Equations

C. Complex linear equations where more than one of the numbers is missing require a lot more work and don't have just one answer.*eg., (3y + 4z) - (2y + 3z) = n*

Method:

The math sentence has to be rearranged so it has just one y and one z.

- remove the brackets – there is a - sign between the brackets so the numbers in the second set of brackets change their signs to negatives
*(3y + 4z) - (2y + 3z) = n*

*3y + 4z - 2y - 3z = n* - group like terms together

*3y - 2y + 4z - 3z = n* - solve for each variable

*1y + 1z = n*

*y + z = n*

### Complicated Equations

D. Complex quadratic equations can be very complicated.*eg., (y² + 3y + 6z) + (3y² + y - 2z) = n*

Even their names can sound complex — the highest power provides the name

eg., n¹, n², n³

- n¹ – linear equation
- n² – quadratic equation
- n³ – cubic equation
- n¹ – quartic equation
- n¹ – quintic equation
- n¹ – polynomial equation

## Evaluating Equations

Teaching Resources for Math for Equations — teaching and practice worksheets.

### Equation Worksheets

Return to Math Skills Index.

## Excited by Equations

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