Leo+DadMade for Leo
Solving & Verifying Equations by Substitution
Rung 2 of 4 · The method

Solve It, Then Prove It

Two stages, every time: solve the equation to find x, then substitute x back in to prove it fits. Let's make the second stage as automatic as the first.


PractiseHit “new equation”, solve for x, then reveal the steps — including the substitution check.
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Audio WalkthroughComing Soon
Video ExplainerComing Soon

Take a two-step equation like 3x + 4 = 19. Solving is two moves; verifying is one more. Three lines of working and you're certain.

Stage One — Solve

Undo the + or −. Take 4 off both sides: 3x = 19 − 4 = 15.

Undo the ×. Divide both sides by 3: x = 15 ÷ 3 = 5. There's your answer.

Stage Two — Verify

Don't stop there. Take x = 5 and slot it back into the original equation, left side only: 3×5 + 4 = 15 + 4 = 19. The right side is also 19. Both sides land on 19, so the answer is verified. Tick it and move on with full confidence.

The habit: after you find x, write one extra line — "Check: substitute x back in." Work out the left side, compare to the right. Equal? Done and trusted.

Show Your Working Both Ways

In an exam, that little check line does two jobs: it catches your own slips, and it shows the marker you understand what a solution is. Use the toy to drill the rhythm — solve in your head or on paper, then hit "show me the steps" and watch the substitution check confirm it. Do a dozen and it stops feeling like extra work.

Us, Thinking Out Loud

Could you talk me through the three lines without looking?

Which feels slower — solving, or checking? Why?