What is an equation?

An equation is a statement that two expressions are equal. The simplest example is 3 + 4 = 7.

The interesting equations are the ones with an unknown:

2x + 1 = 9

Here x is the unknown. Solving the equation means finding every value of x that makes the statement true.

The Golden Rule

You can do anything to one side of an equation, as long as you do exactly the same thing to the other side. That keeps the equality intact.

So to solve 2x + 1 = 9:

1. Subtract 1 from both sides → 2x = 8
2. Divide both sides by 2 → x = 4

Always check by plugging back in: 2 · 4 + 1 = 9 ✅.

Why this matters

Every word problem you will ever face on the SAT, the IELTS quantitative module, or in real life starts by translating a situation into an equation. Get fluent at the moves above and the rest is just translation.