oral/written explanationRe-explain the worked example
Re-explain how to solve 3x + 5 = 20. Name the operation used on both sides at each step.
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Example lesson history · Solving two-step linear equations
Use inverse operations confidently · 26 Aug Keep both sides balanced · 19 Aug Substitute values into expressions · 12 Aug2 September 2026
Solving two-step linear equations ✓ Teacher approved
This lesson focused on solving equations by preserving equality. Instead of ‘moving’ terms across the equals sign, use the inverse operation on both sides. Writing one step per line and keeping the equals signs aligned helps you see that each line has the same value. Always check the final answer by substituting it back into the original equation.
Work from this lesson
Your next steps
written practiceSolve three equations
Solve 2x + 3 = 15, 5x - 4 = 21 and 3x + 8 = 2. Show one operation per line and keep the equals signs aligned.
error analysisRepair the incorrect step
Start from 4x - 7 = 9 and explain why the step 4x = 2 is wrong. Then write the correct steps to reach the solution and check it.
You worked on solving two-step linear equations by keeping both sides equal. For 3x + 5 = 20, you subtracted 5 from both sides, then divided by 3 to get x = 5, and checked it by substitution. You also used the same balance principle for 4x - 7 = 9 and 3x + 8 = 2, including a negative answer, and practised spotting and correcting a sign error.
Use the same operation on both sides
An equation stays balanced only if you do the same thing to both sides. If you subtract 5 from the left, you must subtract 5 from the right too.
Example 3x + 5 = 20 → subtract 5 from both sides → 3x = 15 → divide both sides by 3 → x = 5.
Common misconception A number changes sign when it crosses the equals sign.
Check yourself Can you say which operation you used on both sides at each line?
Inverse operations undo what has happened
Use the inverse operation to undo the effect on x. If 7 has been subtracted, add 7. If something has been added, subtract it. This is about undoing, not about moving numbers across.
Example 4x - 7 = 9 → add 7 to both sides → 4x = 16 → x = 4.
Common misconception Subtracting 7 again is the right next step after seeing -7.
Check yourself What operation reverses the one already done to x?
Check with substitution, even if x is negative
A negative answer is not automatically wrong. Substitute it back into the original equation to test whether both sides are equal.
Example 3x + 8 = 2 → subtract 8 → 3x = -6 → x = -2. Check: 3 × -2 + 8 = 2.
Common misconception A negative value for x means the solution must be wrong.
Check yourself Does your answer make the original equation true when you substitute it?
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Undoing a two-step equationIllustrative preview · not playable
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