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Basic Algebra

Basic Algebra

At a Glance - Algebraic Expressions

Okay, let's clear this up:

An equation is a complete mathematical sentence that includes a sign of equality (like an equal sign). 

 An expression is not a mathematical sentence; it is a mathematical phrase because it doesn't have an equal sign.

5 + 25 + 2 = 7
3x3x = 15
4(5 + 8x)4(5 + 8x) = -44

Let's break it down further.

An expression is made up of terms. Terms are each separate values in an expression. They can be separated by operations, like plus and minus signs.

There are three parts of most expressions: the variable, constant, and coefficient.

Variable: an unknown or changing number. Often represented by “x”.
Constant: a number that doesn’t change
Coefficient: the number that is multiplied by the variable


Names for algebraic expressions

monomial1 Termxy
binomial2 Termsxy - 2x
trinomial3 Termsxy - 2x + 3y
quadnomial4 Termsxy - 2x + 3 y – 1

Here is a chart of common phrases.

Common Words and Phrases for:
more than
in addition to
greater than
less than
take away
twice (×2)
divided by

In these translations we will use the letter x to represent the variable, though any letter, symbol, or emoticon would work. Smiley faces and hearts, anyone?

Expression in WordsExpression in Symbols
a number increased by twelvex + 12
the sum of twice a number and six2x + 6
eighty less than a numberx – 80
twenty-eight split in half28 ÷ 2
the product of a number and seven7x
the quotient of a number and fourx ÷ 4
five greater than three times a number3x + 5
a number distributed evenly among sixx ÷ 6
the total of forty and a number40 + x
three times the total of a number and five3(x + 5)
Equation in WordsEquation in Symbols
A number is negative ten.x = -10
A number plus two is eight.x + 2 = 8
The difference between a number and seven is negative three.x – 7 = -3
One less than twice a number is seventeen.2x – 1 = 17
Twelve is the product of a number and three.12 = 3x
Half of a number is twenty.x × ½ = 20 or ½x = 20
A number is equal to the sum of twice the number and negative three.x = 2x + -3

Look Out: be very careful with "less than". Three less than a number is translated as "x – 3". The reverse of that, "3 – x" would be a number less than three.

Translate each phrase into an algebraic expression or equation.

The sum of twice a number and three times the number is thirty.

Exercise 2

Two times the difference of a number and four.

Exercise 3

Twelve less than a number is equal to the product of the number and five.

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