L4 · One-step equations: x + a = b (integers)

Learning goal

“I can model and solve one-step equations of the form x + a = b where a and b are integers - including negative answers - and verify every solution by substitution.”

Solution — the value of the variable that makes an equation true (e.g. x = -5 is the solution of x + 3 = -2).

Verify — substitute the solution back into the original equation and confirm both sides match.

Integer — a whole number or its negative: ..., -3, -2, -1, 0, 1, 2, 3, ... (review from G7U04).

One-step equation — an equation that can be solved with a single inverse operation.

Worked example

Solve x + 5 = 3. Step 1: Model it: a number, increased by 5, lands on 3. On a number line: the unknown starts somewhere, jumps +5, and ends at 3. Step 2: Undo with the inverse operation (L3): subtract 5 from both sides. x = 3 - 5 = -2. Step 3: Negative answers are legal - 3 - 5 crosses zero and lands at -2. Step 4: Verify by substitution: -2 + 5 = 3. The original claim is true, so x = -2 is the solution. Balance view, in words: removing 5 from both pans still works - on the right pan it takes the pile from 3 down past zero to -2, a debt of 2. Integers let the balance go below zero.

Check yourself — explain it

Why is x = -2 acceptable as a solution to x + 5 = 3?

Paired problem — example still visible

Solve and verify x + 6 = 1. -> x = -5; check: -5 + 6 = 1

Faded completion — last step is yours

"x + 2 = -4: subtract 2 from both sides, so x = -4 - 2 = ___" -> -6

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

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