Ninth Grade · Math · week 2

Solving linear equations

Solve one-variable linear equations, including variables on both sides, by legal moves that keep the balance.

An equation is a balance scale: whatever the left side weighs, the right side weighs the same. The one law of algebra is: whatever you do to one side, do to the other. Add 5 to both sides, the balance holds. Divide both sides by 3, still holds.

To solve, undo what's being done to x — in reverse order of operations. If x was multiplied then added-to, you subtract first, then divide. When x appears on BOTH sides, gather the x-terms on one side first (subtract the smaller x-term from both sides), then finish normally. Every step is reversible — that's what makes it legal.

📋 For the grown-up teacher
Teach it (10–15 min):
  • Get an actual balance image going: draw a scale, put "5x − 4" on one pan and "3x + 10" on the other.
  • Narrate every move as "do it to BOTH sides" — make them say it too, every single step, this week only.
  • Teach the check habit now: substitute the answer back. It's 15 seconds and catches almost everything.
  • Let them pick: distribute first or divide first on 3(x − 2) = 18 — both work; comparing routes builds flexibility.
Talk about it:
  • Why does doing the same thing to both sides keep the equation true?
  • How do you decide what to undo first?
  • What does it mean if you end up with something like 5 = 5? Or 5 = 7?

Mastery looks like: They solve a variables-on-both-sides equation with clean steps and check the answer without being asked.

Common stumbles: Doing a move to only one side; sign slips when subtracting an x-term; declaring victory without checking.

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
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