L4 · Solving equations with inverse operations

Learning goal

“I can solve one-operation equations by applying the inverse operation to both sides - keeping the balance - and verify every solution by substituting it back into the original equation.”

Inverse operation — the operation that undoes another: addition undoes subtraction, and multiplication undoes division.

Solve — to find the value of the variable that makes an equation true.

Solution — that value itself: in x + 7 = 15, the solution is x = 8.

Verify — to substitute the solution back into the ORIGINAL equation and check that both sides are equal.

Worked example

Solve x + 7 = 15. Step 1: How is the 7 attached to x? It is ADDED. Step 2: Apply the inverse to BOTH sides (the balance rule): subtract 7 from both sides. x + 7 - 7 = 15 - 7, so x = 8. Step 3: Verify in the ORIGINAL equation: 8 + 7 = 15. Both sides equal - the solution is right. Second form: n - 5 = 12. The inverse of subtracting 5 is adding 5 to both sides: n = 12 + 5 = 17. Verify: 17 - 5 = 12. Arrow view, in words: x -> (+7) -> 15. Solving walks the arrow backwards: 15 -> (-7) -> 8.

Check yourself — explain it

Why must the inverse operation be applied to both sides, not just the side with x?

Paired problem — example still visible

Solve and verify: y + 4 = 13 -> y = 9; check: 9 + 4 = 13

Faded completion — last step is yours

"k - 6 = 10: add 6 to both sides, so k = 10 + 6 = ___" -> 16

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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