Developing math vocabulary
Equation
Pronunciation: ee-KWAY-zhun
An equation states that two expressions have the same value.
L = RDeveloping
Plain language
What it means
An equation states that two expressions have the same value.
Formal meaning
Mathematical definition
An equation is a proposition of the form L = R; a solution is a value that makes the proposition true.
Where it fits
Its place in mathematics
Equations model balances, constraints, formulas, intersections, motion, finance, geometry, and scientific laws.
Why it matters
The practical reason to learn it
Solving an equation finds values that satisfy a stated relationship.
Worked example
Solve a linear equation
Solve 4x - 3 = 17.
- Add 3 to both sides to get 4x = 20.
- Divide both sides by 4.
x = 5.
Real-life example
Where this appears
A pharmacist may use a verified formula equation to calculate a concentration or quantity.
Common mistake
What to watch for
Moving a term across the equals sign and changing its sign without understanding the inverse operation being applied to both sides.
Memory tip
Keep this in mind
Write each balancing operation on both sides before simplifying.
Little-known fact
Keep curiosity alive
Some equations have one solution, many solutions, no solution, or an entire interval of solutions.
A profession that uses this idea
Formulas express required relationships
Clinical and laboratory calculations use equations whose units and inputs must be checked carefully.
Explore Nurses & PharmacistsFollow the learning trail
Prerequisites, related ideas and next concepts
People behind the ideas
Related Math Heroes
Al-Khwarizmi
A scholar whose systematic writing on calculation and equation solving helped shape algebra and whose name became the root of the word algorithm.
René Descartes
A French thinker who helped unite algebra and geometry by representing curves and shapes with coordinates and equations.
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