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 Depdendent Variable

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 Dependent Variable

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Writing Algebraic Expressions

Many verbal phrases occur repeatedly in applications. The following list of some frequently occurring verbal phrases and their translations into algebraic expressions will help you translate words into algebra.

Translating Words into Algebra

 Verbal Phrase Algebraic Expression Addition: The sum of a number and 8Five is added to a number Two more than a number A number increased by 3 x + 8x + 5 x + 2 x + 3 Subtraction: Four is subtracted from a numberThree less than a number The difference between 7 and a number Some number decreased by 2 A number less than 5 x - 4x - 3 7 - x x - 2 x - 5 Multiplication: The product of 5 and a numberSeven times a number Twice a number One-half of a number 5x7x 2x Division: The ratio of a number to 6The quotient of 5 and a number Three divided by some number

More than one operation can be combined in a single expression. For example, 7 less than twice a number is written as 2x - 7.

Solving Problems

We will now see how algebraic expressions can be used to form an equation. If the equation correctly models a problem, then we may be able to solve the equation to get the solution to the problem. Some problems in this section could be solved without using algebra. However, the purpose of this section is to gain experience in setting up equations and using algebra to solve problems. We will show a complete solution to each problem so that you can gain the experience needed to solve more complex problems. We begin with a simple number problem.

Example 1

A number problem

The sum of three consecutive integers is 228. Find the integers.

Solution

We first represent the unknown quantities with variables. The unknown quantities are the three consecutive integers. Let

 x = the first integer, x + 1 = the second integer, and x + 2 = the third integer.

Since the sum of these three expressions for the consecutive integers is 228, we can write the following equation and solve it

 x + (x + 1) + (x + 2) = 228 The sum of the integers is 228. 3x + 33x x = 228= 225 = 75 x + 1 = 76 Indentify the other unknown quantities. x + 2 = 77

To verify that these values are the correct integers, we compute

75 + 76 + 77 = 228.

The three consecutive integers that have a sum of 228 are 75, 76, and 77.