A linear equation in one variable has the form ax + b = 0. Key concepts: solve using inverse operations, maintain equation balance, isolate the variable. For MCQs, identify variable coefficient and constant term quickly. Common trap: forgetting to change sign when moving terms across equals sign. Exam tip: verify solution by substitution. Shortcut: x = -b/a directly. Applications include cost-revenue problems, speed-distance-time calculations. Always check if solution is valid within problem context. Practice with word problems to master quick conversions from narrative to equation form. Standard form is ax + b + c = 0 where solutions are real and single valued.