Linear equations without losing the sign

Most linear-equation mistakes are not big conceptual gaps. They are tiny bookkeeping slips: a minus sign moves, a term crosses the equals sign twice, or both sides are not treated equally.

The main idea

Write the operation you apply to both sides, then simplify only after the operation is visible. This keeps the equation equivalent at every line.

A short example

For $3x-7=11$, add $7$ to both sides first, then divide by $3$.

Check while you solve

• Circle the term containing the variable.
• Undo addition or subtraction before multiplication or division.
• Substitute the answer into the original equation, not the last line.