Math Foundations
Algebra

Solving One- and Two-Step Equations

Solving an equation means finding the value that makes it true — by undoing whatever's been done to the variable, one operation at a time, while keeping both sides balanced.

An equation is a claim that two things are equal. Whatever you do to one side, you must do to the other — otherwise the two sides stop being equal. Solving means using inverse operations to peel away everything surrounding the variable: undo addition with subtraction, undo multiplication with division, and so on, until the variable is alone on one side.

Order matters when there are two steps. Undo addition and subtraction first, then multiplication and division — the reverse of order of operations, since you’re unwinding the expression instead of building it.

Solving 3x + 7 = 22

Two operations were done to x to build this equation — multiplied by 3, then had 7 added. Solving means undoing them in reverse order: subtract first, divide second.

Start with the equation
3x + 7 = 22

Start with 3x + 7 = 22. First, undo the +7 by subtracting 7 from both sides.

When the equation has parentheses, distribute first to clear them — then it’s back to the same two-step process:

Worked example: 2(x − 3) = 10
= 2x − 6 = 10
= 2x = 16
= x = 8
Common mistake
Dividing or multiplying before subtracting or adding, breaking the equation into a mess of fractions. For 3x + 7 = 22, dividing everything by 3 first gives x + 7/3 = 22/3 — not technically wrong, but far more likely to introduce an arithmetic error. Undo addition and subtraction first, multiplication and division second.
Question 1 of 9easy
Solve: x + 7 = 12