Solving Two-Step Equations: notes and common mistakes

Key ideas

• An equation is a balance. Do the same thing to both sides.
• Undo operations in reverse order. For equations shaped like ax + b = c, that means add/subtract first, then multiply/divide.
• Inverse operations: addition and subtraction undo each other; multiplication and division undo each other.
• Always check your answer by substituting it back into the original equation.

Steps

1. Circle the variable term and the constant.
2. Undo the add or subtract on both sides (for ax + b = c).
3. Undo the multiply or divide on both sides.
4. Check by substituting.

Formulas

• Pattern: ax + b = c gives x = (c − b) ÷ a (when a ≠ 0)

Watch out

• Do the move to both sides, not just the side with the variable.
• Watch signs: in x − 4 = 3 you add 4.
• Watch the signs when you divide by a negative: a negative ÷ a negative is positive (−3x = −15 gives x = 5), but a positive ÷ a negative is negative (−2x = 6 gives x = −3).

Why it works

• Why the same thing to both sides? Equal things stay equal when you treat them equally.
• Why add or subtract first? The constant was attached last, so it has to come off first. Otherwise you must divide every term.