L5 · One-step equations: ax = b and x/a = b

Learning goal

“I can model and solve one-step equations of the forms ax = b and x/a = b (whole numbers throughout), and verify every solution by substitution.”

Coefficient — the number multiplying the variable in a term: in 4x, the coefficient is 4.

Whole number — 0, 1, 2, 3, ... - the counting numbers and zero. In this lesson a, b and the answers are whole numbers.

Inverse operation — division undoes multiplication; multiplication undoes division (review from L3, now the main tool).

Arrow diagram — a picture of an operation as an arrow (x -x4-> 4x) and its undoing as the reverse arrow (4x -/4-> x).

Worked example

Solve 3x = 18. Step 1: Draw the arrow: x -x3-> 18. Solving means walking the arrow BACKWARDS. Step 2: The reverse of x3 is /3. Apply it to both sides (preservation of equality): x = 18 / 3 = 6. Step 3: Verify by substitution: 3(6) = 18. Balance view, in words: three identical bags balance 18 marbles; one bag balances 18 / 3 = 6. The arrow and the balance are the same idea in two costumes.

Check yourself — explain it

Why do we divide by the coefficient to solve ax = b?

Paired problem — example still visible

Solve and verify 5x = 45. -> x = 9; check: 5(9) = 45

Faded completion — last step is yours

"6x = 42: x = 42 / 6 = ___" -> 7

Ready to practise?

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

Start practice →Take the unit quiz