equation
equation — noun
1. a written statement in mathematics that uses symbols and an equals sign to show
a written statement in mathematics that uses symbols and an equals sign to show that two sets of numbers or quantities are the same in value.
The teacher wrote the equation 3x + 5 = 20 on the board for the class to solve.
countable: solve + equation
Kevin spent the whole evening working on a quadratic equation from his maths homework.
A simple linear equation such as y = 2x + 1 represents a straight line on a graph.
The students checked their answer by putting the number back into the original equation.
To find the unknown value, you must isolate x on one side of the equation.
文法句型
equation + equals sign + result
用法筆記
A mathematical equation always contains an equals sign (=) and expresses a relationship between two sides. By contrast, an expression (such as 3x + 5) has no equals sign.
常見錯誤
2. a written representation of a chemical reaction using symbols and formulas that
a written representation of a chemical reaction using symbols and formulas that shows which substances react and what new substances are produced.
The chemical equation for burning methane is CH4 + 2O2 → CO2 + 2H2O.
domain: chemistry — chemical equation
Amani balanced the chemical equation by adjusting the number of each type of molecule.
collocation: balance + equation
The students wrote a chemical equation to show how iron combines with oxygen.
The equation showed that two hydrogen atoms react with one oxygen atom to form water.
Stephanie drew an arrow in the chemical equation to show the direction of the reaction.
- chemical formula
a formula shows the composition of a single substance (e.g. H₂O); an equation shows the transformation between multiple substances
文法句型
equation + arrow + product
用法筆記
A chemical equation uses an arrow (→) rather than an equals sign (=). The substances on the left are reactants; those on the right are products. Distinguish from equation/1 (mathematical), which uses numbers and an equals sign.
常見錯誤
3. a set of connected factors or issues that you need to think about together to un
a set of connected factors or issues that you need to think about together to understand something or decide what to do.
When planning the wedding, the budget equation included the venue, the food, and the flowers.
metaphorical: the + noun + equation
The political equation in the region became more complicated after the new trade agreement.
Emre realised that time was the missing part of the equation for finishing his project.
Hiring new staff changes the equation because we must cover extra salaries and training.
The peace equation involves trust from both sides, not just a signed document.
- situation
more general — equation emphasises that multiple factors interact and need to be weighed together
- scenario
scenario suggests a possible or imagined set of events; equation focuses on the balancing of factors
- mix
informal — a mix of ingredients/factors is similar, but equation has the added sense of trade-offs and balance
文法句型
the + equation + of + factors
part of the equation
用法筆記
This is a metaphorical extension of the mathematical sense. Often used with the definite article ('the equation') or a possessive ('our equation'). Common in business, politics, and everyday decision-making contexts.
常見錯誤
4. the process of viewing two separate items as equal in value, meaning, or importa
the process of viewing two separate items as equal in value, meaning, or importance.
The simple equation of wealth with happiness is a common but misleading belief in society.
pattern: the equation of X with Y
Marta rejected the easy equation of success with a large salary or a fancy title.
The manager's equation of hard work with long hours frustrated employees who worked efficiently.
Critics warned against the equation of patriotism with unquestioning support for government policies.
Aarav argued that the equation of intelligence with exam results ignores creativity and practical skills.
- identification
suggests seeing two things as essentially identical; equation allows for comparison without full identity
- comparison
broader — comparison examines similarities and differences; equation asserts sameness
- distinction
the act of pointing out differences rather than treating things as the same
文法句型
the equation of X (with) Y
用法筆記
Typically used in fixed constructions with 'of … and …' or 'of … with …'. Frequently appears in academic or formal writing about concepts, ideologies, or values. The focus is on the act of mentally putting two things in the same category.