What a two-step equation actually asks
An equation is a statement that two expressions have the same value. Solving it means finding the number that makes the statement true. In 2x + 7 = 19, the left side has been built from x by two operations: multiply by 2, then add 7. Solving simply means undoing those operations in reverse order.
That reverse order matters. When you build the expression you multiply first and add second, so when you take it apart you subtract first and divide second — the same way you take off your shoes before your socks only in reverse.
The method, step by step
Use this sequence on every two-step equation and you will never have to guess what to do next.
- Identify the constant that is added or subtracted on the variable side (here, +7).
- Do the opposite operation to both sides: 2x + 7 - 7 = 19 - 7, giving 2x = 12.
- Identify the number multiplying the variable (here, 2).
- Divide both sides by it: 2x / 2 = 12 / 2, giving x = 6.
- Check by substituting back: 2(6) + 7 = 12 + 7 = 19. True, so x = 6 is correct.
Worked example with a negative coefficient
Solve -3x - 4 = 11. Add 4 to both sides: -3x = 15. Divide both sides by -3: x = -5. Check: -3(-5) - 4 = 15 - 4 = 11. Correct.
The only new idea here is that dividing by a negative number flips the sign of the answer. Nothing else about the method changes, which is why practising the checking step is worth more than memorising special cases.
Four mistakes that lose the most marks
Almost every wrong answer in this topic comes from one of these four, and all four are avoidable with a habit rather than more talent.
- Doing the operation to one side only — the equation stops being true immediately.
- Dividing before subtracting, which forces you to divide the constant too and usually produces fractions you did not need.
- Losing a negative sign when moving a term across, especially with subtraction.
- Skipping the substitution check, which catches almost every arithmetic slip in under ten seconds.
Practice set (answers below)
Solve each and check by substitution: (a) 5x + 3 = 28, (b) 4x - 9 = 7, (c) -2x + 6 = 14, (d) x/3 + 5 = 9, (e) 7 - 2x = 1.
Answers: (a) x = 5, (b) x = 4, (c) x = -4, (d) x = 12, (e) x = 3. If you missed one, redo it from a blank line rather than reading the solution again — reproducing the steps is what makes them stick.