An equation is a number sentence stating that two expressions have the same value. The difference between an expression and an equation is the equal sign, . If a problem is stated verbally, the first step in solving is to translate the description of the problem into an algebraic equation.
Some words and phrases that represent the equal sign include:
- Amounts to
- Is the same as
To translate a problem description into an equation, look for the word or phrase that represents the equal sign. Determine what part of the problem describes the expression on each side. Translate the two expressions, and place the equal sign between them.
Writing Algebraic Equations
A library has 86 science fiction paperbacks and e-books combined. The number of paperbacks are 4 fewer than twice the number of e-books.
Write an equation that represents the combined number of science fiction paperbacks and e-books.
Choose a variable.The number of paperbacks is described in relation to the number of e-books. So, let represent the number of e-books:
Application of Equations
Write the values using the appropriate units of measure.
The perimeter is 46 cm.
The area is 120 square centimeters.
Eve opens an account with $100. The account earns 6% interest compounded monthly. How much will be in the account after 5 years?Use the formula for compounded interest, or interest that is added back into the amount that earns interest.
The original amount in the account is $100, or .
The rate, , of 6% expressed as a decimal is 0.06.
The time, , is years.