Lesson 1: Writing Equations in One Variable

Property

An expression is a mathematical phrase that contains numbers, variables, and operations but has no equal sign: $3x + 5$ or $2y - 7$.

An equation is a mathematical sentence that shows two expressions are equal using an equal sign: $3x + 5 = 14$ or $2y - 7 = 11$.

Property

Operation keywords: sum ($+$), difference ($-$), product ($\times$), quotient ($\div$)

Equal sign keywords: is, equals, the same as, results in ($=$)

Property

To translate a word problem into an equation, start by identifying an unknown and use a variable to represent it.
Next, identify what you do know (the given numbers).
Finally, determine what connects the two pieces of information together to write an algebraic expression that represents the situation.

Examples

• 'Twice a number ($n$) decreased by 7 is 21.' This translates to the equation $2n - 7 = 21$.

• 'A family buys 3 tickets that cost $x$ dollars each and pays a 5 dollar parking fee, for a total of 50 dollars.' This translates to $3x + 5 = 50$.