What Is an Equation?

≈ 20 min

An equation is a mathematical statement that two expressions are equal. It always contains an equals sign.

3x + 4 = 19

The letter $x$ is a variable — a placeholder for a number we do not know yet. Solving an equation means finding every value of the variable that makes the statement true. Here $x = 5$ works, because $3(5) + 4 = 19$ .

Compare this with an expression like $3x + 4$ on its own: an expression has no equals sign, so there is nothing to solve — it can only be simplified or evaluated.

Which of the following is an equation?

$7x - 2$

$3x + 4 = 19$

$5(x + 1)$

$x^2 - 9$

By inspection (just thinking, no written method): what value of $x$ makes $x + 2 = 5$ true?

An equation is like a level balance scale because…

the left side is always bigger

both sides have the same value

it always contains $x$

it can never change