Leo+DadMade for Leo
Solving Linear Equations
Rung 3 of 4 · The traps

Right Order, and Mind the Minus

Two slips cost almost all the lost marks here: undoing things in the wrong order, and fumbling a negative. Let's make both impossible to fall for.


ExplorePick which move to make first. Get the order or the sign wrong and it’ll tell you why.
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Audio WalkthroughComing Soon
Video ExplainerComing Soon

The method from rung 2 is sound — the trouble is people apply it in the wrong order or lose track of a sign. Both are fixable habits, not talent problems.

Trap One: the Order

It's tempting to divide first when you see 2x + 3 = 11 — but that's wrong, because the + 3 wasn't multiplied by 2, it was added on afterwards. You must undo the +/− before the ×/÷ (reverse BODMAS). Strip the + 3 away to get 2x = 8 first, then divide. In the toy, picking "÷ 2 first" will stop you and explain why.

Say it plainly: the last thing done to x is the first thing you undo. Adding/subtracting was done last, so undo it first — then deal with the multiply.

Trap Two: the Negatives

Two sign-traps hide in here. First, to undo a subtraction you add — so 2x − 3 = 7 needs + 3 on both sides, not another subtract. Second, if the number multiplying x is negative — say −2x = 8 — dividing by −2 flips the sign of the answer: x = −4. The toy throws negatives at you on purpose and flags when the sign flips.

The Safety Check

If you're ever unsure, do the same move to both sides and ask "did I do the opposite operation?" Subtraction undoes addition; division undoes multiplication; and a negative divided by a negative is positive. Slow down on the sign and the order, and these two traps simply stop happening.

Us, Thinking Out Loud

Why must we undo the + or − before the ×?

What happens to the sign when we divide by a negative?