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Absolute Values
Solving Two-Step Equations Algebraically
Multiplying Monomials
Factoring Trinomials
Solving Quadratic Equations
Power Functions and Transformations
Composition of Functions
Rational Inequalities
Equations of Lines
Graphing Logarithmic Functions
Elimination Using Multiplication
Multiplying Large Numbers
Multiplying by 11
Graphing Absolute Value Inequalities
The Discriminant
Reducing Numerical Fractions to Simplest Form
Addition of Algebraic Fractions
Graphing Inequalities in Two Variables
Adding and Subtracting Rational Expressions with Unlike Denominators
Multiplying Binomials
Graphing Linear Inequalities
Properties of Numbers and Definitions
Factoring Trinomials
Relatively Prime Numbers
Rotating a Hyperbola
Writing Algebraic Expressions
Quadratic and Power Inequalities
Solving Quadratic Equations by Completing the Square
BEDMAS & Fractions
Solving Absolute Value Equations
Writing Linear Equations in Slope-Intercept Form
Adding and Subtracting Rational Expressions with Different Denominators
Reducing Rational Expressions
Solving Absolute Value Equations
Equations of a Line - Slope-intercept form
Adding and Subtracting Rational Expressions with Unlike Denominators
Solving Equations with a Fractional Exponent
Simple Trinomials as Products of Binomials
Equivalent Fractions
Multiplying Polynomials
Graphing Equations in Three Variables
Properties of Exponents
Graphing Linear Inequalities
Solving Cubic Equations by Factoring
Adding and Subtracting Fractions
Multiplying Whole Numbers
Straight Lines
Solving Absolute Value Equations
Solving Nonlinear Equations
Factoring Polynomials by Finding the Greatest Common Factor
Algebraic Expressions Containing Radicals 1
Addition Property of Equality
Three special types of lines
Quadratic Inequalities That Cannot Be Factored
Adding and Subtracting Fractions
Coordinate System
Solving Equations
Factoring Polynomials
Solving Quadratic Equations
Multiplying Radical Expressions
Solving Quadratic Equations Using the Square Root Property
The Slope of a Line
Square Roots
Adding Polynomials
Arithmetic with Positive and Negative Numbers
Solving Equations
Powers and Roots of Complex Numbers
Adding, Subtracting and Finding Least Common Denominators
What the Factored Form of a Quadratic can tell you about the graph
Plotting a Point
Solving Equations with Variables on Each Side
Finding the GCF of a Set of Monomials
Completing the Square
Solving Equations with Radicals and Exponents
Solving Systems of Equations By Substitution
Adding and Subtracting Rational Expressions
Laws of Exponents and Dividing Monomials
Factoring Special Quadratic Polynomials
Solving Quadratic Equations by Completing the Square
Reducing Numerical Fractions to Simplest Form
Factoring Trinomials
Writing Decimals as Fractions
Using the Rules of Exponents
Evaluating the Quadratic Formula
Rationalizing the Denominator
Multiplication by 429
Writing Linear Equations in Point-Slope Form
Multiplying Radicals
Dividing Polynomials by Monomials
Factoring Trinomials
Introduction to Fractions
Square Roots
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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 8

Five is added to a number

Two more than a number

A number increased by 3

x + 8

x + 5

x + 2

x + 3

Subtraction: Four is subtracted from a number

Three less than a number

The difference between 7 and a number

Some number decreased by 2

A number less than 5

x - 4

x - 3

7 - x

x - 2

x - 5

Multiplication: The product of 5 and a number

Seven times a number

Twice a number

One-half of a number




Division: The ratio of a number to 6

The 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.


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 + 3



= 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.

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