L6 · Solving and verifying one- and two-step equations

Learning goal

“I can solve an equation of one or two steps by using inverse operations to keep the balance, and I can VERIFY my solution by substituting it back into the original equation.”

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

Solution — the value of the variable that makes an equation true: x = 8 solves x + 7 = 15.

Verify — check a solution by substituting it back into the original equation and confirming both sides are equal.

Worked example

Solve x + 7 = 15. Step 1: The balance: x and a 7-weight on the left, 15 on the right. Step 2: Undo the +7 with its inverse, -7 - applied to BOTH sides to keep the balance: x + 7 - 7 = 15 - 7, so x = 8. Step 3: VERIFY. Substitute 8 into the original: 8 + 7 = 15. Both sides equal - 8 is the solution. Second quick model: 3x = 21. Undo x 3 with / 3 on both sides: x = 7. Verify: 3 x 7 = 21. Whatever you do to one side, you do to the other - that is what keeps the equation true while you unwrap the variable.

Check yourself — explain it

To solve x + 7 = 15, we subtract 7 from both sides because...

Paired problem — example still visible

Solve and verify: 4n = 28 -> n = 7 (/ 4 both sides; verify 4 x 7 = 28)

Faded completion — last step is yours

"m + 9 = 20: subtract ___ from both sides, so m = ___; check: ___ + 9 = 20" -> 9; 11; 11

Ready to practise?

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

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