# Equations that Describe Patterns

## Key Questions

An equation is a statement that two expressions are equal, so we have:

$\text{expression = expression}$

#### Explanation:

An expression is a maths sentence made up of terms which can have numbers and or variables as factors.

$3 x , \text{ "3x+5," } 2 {x}^{2} - 5 x + 3$ are all examples of expressions.

An equation is a statement that two expressions are equal, so we have:

$\text{expression = expression}$

An equation is solved, which means to find the value(s) of the variable(s) which makes the equation true,

$3 x - 5 = 22 \text{ } \rightarrow x = 9$

${x}^{2} + 4 x - 45 = 0 \text{ } x = - 9 \mathmr{and} x = 5$

An equation which contains two or more variables does not have a unique solution, but rather many, many solutions,

$x + y = 10$ has infinitely many solutions.

is, equals, is equal to

#### Explanation:

The product of $4$ and $3$ is $12$.

The product of $4$ and $3$ equals $12$.

The product of $4$ and $3$ is equal to $12$.

$4 \cdot 3 = 12$