Equation Solving Worksheets

One-step, two-step, or both on the same page

One-step equations come in four shapes: x + a = b, x − a = b, ax = b, and x ÷ a = b. One operation to undo, and the whole lesson is recognising which one.

Two-step equations are all of the form ax + b = c or ax − b = c. Two operations, and now the order matters — undo the addition first, then the multiplication, which is the reverse of the order they appear in.

Mixed puts both on the sheet. Worth doing once two-step is secure, because deciding how many steps a problem needs is itself a skill and a page of nothing but two-steps never asks for it.

Every answer has been checked against its own equation

Problems are built backwards from a chosen value of x, so the equation is constructed to have that answer rather than solved after the fact. There is no rounding anywhere and every solution is a whole number.

That last point is deliberate. An equation whose answer is 2.4 is not harder algebra, it is the same algebra plus decimal arithmetic, and it turns a mistake in the method into a mistake in the division. Keep those separate while the method is being learned.

Negatives change the sheet more than the setting suggests

Switch them on and about a third of the answers become negative, with the right-hand side printed in brackets when it is negative: 3x + 7 = (−2).

This is where most of the errors in the whole topic live. A pupil comfortable with 3x + 7 = 22 will routinely produce x = 3 for 3x + 7 = −2, because the sign gets dropped somewhere in the middle. Leave negatives off until the positive case is automatic, then turn them on and expect the marks to fall.

The coefficient cap

Between 2 and 20. It bounds the numbers in the equation and the size of the answer.

Low, at 5 or 6, and the arithmetic disappears entirely, which is what you want when the method is new — a pupil who fails at 3x = 12 has an algebra problem, not a times-tables one. High, at 20, and correct method still needs correct arithmetic to produce a correct answer, which is closer to an exam.

What the form offers

Mode, coefficient cap (2–20), negatives on or off, problems per sheet (1–40), the answer key, a title and Name and Date fields. A4 or US Letter.

The habit worth building

Substitute the answer back in. Every equation on this sheet can be checked in about five seconds, and a pupil in the habit of checking catches their own sign errors without you.

It also changes what the answer key is for. Instead of being the source of truth, it becomes the thing you compare with after you have already convinced yourself — which is what solving an equation is supposed to feel like.

Print at 100% on A4 or US Letter.