Two-Step Equations

For 3x + 5 = 20, work backwards through the order of operations.

Building the expression, you would multiply by 3 first and then add 5. Undoing it, you reverse that: subtract 5 first, then divide by 3.

3x + 5 = 20
3x = 15 (subtracted 5)
x = 5 (divided by 3)

Think of it as unwrapping a parcel: the last layer on is the first layer off.

Isolating a variable means inverting a composition of functions, and inverses compose in reverse order: if f(x) = 3x + 5 is "multiply by 3, then add 5", then f⁻¹(y) = (y − 5)/3 is "subtract 5, then divide by 3."

That reversal is the reason additive terms come off before multiplicative ones in a standard two-step equation — it is the order of operations run backwards, not an arbitrary rule.

An alternative valid route is to divide everything by 3 first, giving x + 5/3 = 20/3. It reaches the same answer but introduces fractions immediately, which is why the standard order is preferred in practice. When the equation is 3(x + 5) = 20 the situation inverts: there, dividing by 3 first is the cleaner move, because the parentheses change which operation was applied last.