A two-step equation needs two inverse operations to isolate the variable. The arithmetic is easy; the part students get wrong is the order, because you undo the operations in the reverse of the order they were applied.
ax + b = c → x = (c − b) ÷ a
Read the equation as a set of instructions applied to x: first multiply by a, then add b. To undo it, reverse the list and reverse each operation, so subtract b first and then divide by a. Whatever you do to one side, you do to the other.
Solve 2x + 5 = 17.
Answer: x = 6
Solve −3x + 7 = 1.
Answer: x = 2
Solve 3(x − 2) = 15.
Answer: x = 7
Work through these in order. Each answer opens to show the full method, so you can check your reasoning rather than just your final number.
Solve: 2x + 3 = 11
Answer: x = 4
Subtract 3: 2x = 8. Divide by 2: x = 4.
Solve: 5x − 4 = 16
Answer: x = 4
Add 4: 5x = 20. Divide by 5: x = 4.
Solve: 3x + 9 = 24
Answer: x = 5
Subtract 9: 3x = 15. Divide by 3: x = 5.
Solve: x/2 + 1 = 6
Answer: x = 10
Subtract 1: x/2 = 5. Multiply by 2: x = 10.
Solve: −2x + 8 = 2
Answer: x = 3
Subtract 8: −2x = −6. Divide by −2: x = 3.
Solve: 4(x + 1) = 20
Answer: x = 4
Divide by 4: x + 1 = 5. Subtract 1: x = 4.
Solve: 7 − 2x = 1
Answer: x = 3
Subtract 7: −2x = −6. Divide by −2: x = 3.
Solve: x/3 − 4 = −1
Answer: x = 9
Add 4: x/3 = 3. Multiply by 3: x = 9.
A taxi charges $3 plus $2 per mile. A trip cost $17. How many miles?
Answer: 7 miles
2m + 3 = 17. Subtract 3: 2m = 14. Divide by 2: m = 7 miles.
Solve: 2(3x − 1) = 16
Answer: x = 3
Divide by 2: 3x − 1 = 8. Add 1: 3x = 9. Divide by 3: x = 3.
Generate a two-step equations test at the grade and difficulty you need, with a complete worked answer key and equivalent versions for retakes.
Prefer free practice first? free equation worksheets with answers
In 2x + 5 = 17, the expression was built by taking x, multiplying by 2, then adding 5. Solving means dismantling it, and you dismantle in the opposite order to how it was built: remove the 5 first, then the 2. This mirrors taking off shoes before socks, and stating it that plainly helps more students than any acronym does.
Once students see solving as undoing a list of instructions in reverse, three-step and four-step equations need no new teaching. They also stop guessing which operation to do first, which is where nearly all of the lost marks in this topic come from.
In 3(x − 2) = 15 the bracket was formed first and the multiplication applied to the whole of it, so dividing by 3 is the correct opening move. Students who expand first will get 3x − 6 = 15 and reach the same answer, which is fine, but it takes an extra line and creates an extra chance to lose a sign.
The rule worth teaching is that if the bracket is multiplied by a number that divides the right-hand side cleanly, divide first. If it does not divide cleanly, expand. Both routes are valid, and choosing deliberately is faster than always doing the same thing.
✗ Dividing before undoing the addition, for example dividing 2x + 5 = 17 by 2 to get x + 5 = 8.5.
✓ Dividing must apply to every term. Remove the constant first, or divide all three terms consistently.
✗ Applying an operation to only one side of the equation.
✓ An equation is a balance. Whatever you do to the left must be done to the right, every time.
✗ Losing the sign when dividing by a negative coefficient.
✓ Dividing a negative by a negative gives a positive. Write the division out rather than doing it mentally.
✗ Never checking the solution.
✓ Substituting the answer back takes ten seconds and catches almost every arithmetic slip.