What is an Equation? Revision Notes for Junior Cert Mathematics

What is an Equation?

An equation is a mathematical expression that shows two things are equal.

It always has an equals sign (=) in it.

infoNote

For example:

$y + 6 = 0$

$3(x - 3) = 12$

$\frac{2x + 2}{4} = \frac{x - 3}{3}$

$2x^2 + 3x - 2 = 0$

Each of these is an equation because they all include an equals sign (=), which shows that the expressions on either side have the same value.

:::

infoNote

Key Theory: In an equation, the left side of the equals sign is the same as the right side.

Equations often include unknowns (letters like x or y) that we need to find. These unknowns are what make solving equations interesting! Our goal when solving an equation is to find the value of the unknown (like x or y) that makes both sides of the equation equal.

infoNote

Application of Theory: Here's how we can apply that theory to the equation y + 6 = 0:

This is an equation because there is an equals sign, which shows that the value on the left side (y + 6) is the same as the value on the right side (0).

The goal is to figure out what y must be to make this equation true.

Right now, with just 6 = 0, this isn't true: 6 is not the same value as 0.

So, we need to find a value for y that, when added to 6, will make the left side equal to 0.

How to solve equations

To solve an equation, we want to find out what value the unknown (like x) should be so that both sides of the equation are equal**.**

We can do this by adding, subtracting, multiplying or dividing both sides of the equation by the same value.

To solve equations step by step:

Multiply out any brackets using the distributive property
Multiply or divide the same number to both sides of the equation
Add or subtract the same number to both sides of the equation

infoNote

Don't worry if you don't understand these steps! They will be covered in detail in the next note!

What types of equations will we learn about?

We will focus on understanding and solving different types of equations:

Linear equations: These are equations where the unknown (like x) is not raised to any power (it's just x).
Equations with fractions: Sometimes equations involve fractions. We will learn how to solve these step by step.
Forming and solving equations: You'll learn how to create equations from word problems and then solve them.
Quadratic equations: These are a bit more complex because the unknown (like x) is squared $(x^2)$ , but don't worry—we'll work through these together.

What is an Equation? (Junior Cert Mathematics): Revision Notes