Seventh Grade · Math · week 20

Two-step equations

Solve two-step linear equations of the form px + q = r, including negative and fractional coefficients, using inverse operations.

A two-step equation takes exactly two moves to solve: first undo any addition or subtraction, then undo any multiplication or division. Always undo in that order -- addition/subtraction first, multiplication/division second -- even when the numbers are negative or fractions.

Every move must be done to BOTH sides of the equation, keeping the balance true. Checking your answer by substituting it back into the ORIGINAL equation takes ten seconds and catches nearly every mistake.

📋 For the teacher
Teach it (10–15 min):
  • Say the order out loud every time: "undo addition or subtraction first, then undo multiplication or division."
  • Keep the balance-scale picture handy -- whatever happens to one side must happen to the other.
  • Build the check-your-answer habit right now, in week one of equations, so it becomes automatic all year.
  • Do not skip fractional or negative coefficients this week -- they follow the exact same two steps as whole positive numbers.
Talk about it:
  • Why do you undo addition or subtraction before multiplication or division?
  • How do you check whether a solution to an equation is correct?
  • What changes about the steps when the coefficient of x is negative?

Mastery looks like: They solve a two-step equation with any combination of signs, including fractional coefficients, and check the result.

Common stumbles: Undoing the operations in the wrong order; performing a move on only one side of the equation.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

FractionsSlice bars and circles into equal parts and compare them.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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