L5 · Two-operation equations: solve and verify

Learning goal

“I can solve equations with two operations by undoing them in reverse order - the constant term first, then the coefficient or divisor - and verify the solution by substituting it into the original equation and evaluating both sides.”

Two-operation equation — an equation where two operations act on the variable, like 3n + 4 = 19 or n/2 + 3 = 8.

Reverse order — solving undoes the operations in the opposite order from how they were applied: last applied, first undone.

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

Solution — the value of the variable that makes the equation true - proven by verification.

Worked example

Solve 3n + 4 = 19. Step 1: Read the arrow chain forward: n -> (x3) -> (+4) -> 19. The +4 was applied LAST. Step 2: Undo the last operation first: subtract 4 from both sides: 3n = 15. Step 3: Now it is a one-operation equation (L4): divide both sides by 3: n = 5. Step 4: Verify in the ORIGINAL: 3(5) + 4 = 15 + 4 = 19. Both sides equal. Say it plainly: forward you multiply then add; backward you subtract then divide. Reverse order is not a trick - it peels off the outermost layer first.

Check yourself — explain it

Why do we subtract 4 before dividing by 3 in 3n + 4 = 19?

Paired problem — example still visible

Solve and verify 2n + 7 = 21 -> n = 7; check: 2(7) + 7 = 14 + 7 = 21

Faded completion — last step is yours

"4k + 6 = 30: subtract 6 -> 4k = 24; divide by 4 -> k = ___" -> 6

Ready to practise?

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

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