L6 · Two-step equations: ax + b = c

Learning goal

“I can model and solve two-step equations of the form ax + b = c (whole numbers throughout) by undoing the operations in reverse order, and verify by substitution.”

Two-step equation — an equation needing two inverse operations to isolate the variable, like 3x + 4 = 19.

Reverse order — solving undoes operations in the opposite order to the one in which they were applied: the last thing done to x is the first thing undone.

Coefficient — the number multiplying the variable (review from L5): in 3x + 4, the coefficient is 3.

Substitution check — replacing the variable with your answer in the original equation to prove both sides match (the verifying habit from L3-L5).

Worked example

Solve 3x + 4 = 19. Step 1: Read the forward story of x: first x was MULTIPLIED by 3, then 4 was ADDED. Two arrows: x -x3-> 3x -+4-> 19. Step 2: Walk backwards, so undo the LAST arrow first: subtract 4 from both sides: 3x = 15. Step 3: Now it is an L5 equation. Undo x3: divide both sides by 3: x = 5. Step 4: Verify in the ORIGINAL: 3(5) + 4 = 15 + 4 = 19. Say it plainly: building the equation dressed x up - x3, then +4. Solving undresses it in the reverse order - -4, then /3. Like unwrapping: last layer on, first layer off.

Check yourself — explain it

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

Paired problem — example still visible

Solve and verify 2x + 7 = 15. -> 2x = 8, so x = 4; check: 2(4) + 7 = 15

Faded completion — last step is yours

"5n + 3 = 28: subtract 3 from both sides to get 5n = 25, then n = ___" -> 5

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