Brackets and sign traps

Expand before solving

When an equation contains brackets, you must first expand them (by distributing the multiplication) before applying the usual rules.

Example: 3(x + 2) = 15 -> 3x + 6 = 15 -> 3x = 15 - 6 = 9 -> x = 3

Pitfall No. 1: the minus sign in front of a set of brackets

When a minus sign precedes a set of brackets, you must change the sign of EVERY term inside them.

Example: 5 - (x - 3) = 2x -> 5 - x + 3 = 2x (note: -x and +3, not -x and -3) -> 8 - x = 2x -> 8 = 2x + x = 3x -> x = 8/3

Pitfall No. 2: Dividing by a negative coefficient

Example: -2x = 8 -> x = 8 / (-2) = -4

Common mistake: forgetting the sign and answering x = 4 instead of x = -4. The sign of the coefficient must always be retained when dividing.

Summary table of pitfalls

Pitfall	Common mistake	Best practice
Term moving to the other side of the equation	Forgetting to change its sign	+ becomes -, - becomes +
Minus sign before a parenthesis	Changing only one sign inside the parenthesis	Changing the sign of all terms
Division by a negative number	Forgetting the sign of the result	Always divide whilst retaining the sign

Getting into the habit of checking your solution by substituting it back into the original equation allows you to spot almost all of these errors.