Solving Equations with Flow Diagrams

An equation has an equals sign, so it can be solved — we find the value of the letter that makes it true. A neat Grade 7 method is the flow diagram: write the operations that build the expression, then reverse them to undo it.

Worked example. Solve $2x + 1 = 9$.

Forward flow (what was done to $x$):

Reverse flow (undo, in the opposite order, using inverse operations):

So $x = 4$. Check: $2(4) + 1 = 9$. ✓

Exam checkpoint

An equation says two quantities are equal. Solve it by undoing the operations around the unknown in reverse order, and do the same thing to both sides. After finding a value, substitute it back; a quick check is part of a complete exam answer.

Short worked example. For $2x+5=17$, subtract 5 to get $2x=12$, then divide by 2: $x=6$. Check: $2(6)+5=17$.