# algebra: chapter 1

## 31 terms

### opposite

additive inverse of any number b is -b if b is positive then -b is negative, if -b is positive then b is negative

### reciprocal

multiplicative inverse of any non zero number b is 1/b

### numerical expressions

consists of numbers, operations, and grouping symbols

### power

repeated multiplication of the same factor

### exponent

represents the number of times the base is used as a factor

### variable

is a letter that is used to represent one or more numbers

### terms

variable terms with x and constant terms with no variables, in an expression that can be written as a sum, the parts added together are called terms

### coefficient

a number that multiplied the variable

### equation

a statement that two expressions are equal

### linear equations

one variable is an equation that can be written in the form of ax + b = 0 where a and b are constants and a is not equal to 0

### solution

a number is a solution of an equation in one variable if substituting the number for the variable results in a true statement

### equivalent equation

two equations are equivalent if they have the same solutions

### formula

is an equation that relates two or more quantities usually represented by variables

### solve for a variable

rewrites an equation as an equivalent equation in which the variable is on one side and does not appear on the other side

a word equation

### linear inequality

an expression in one of the following forms where a and b are real numbers and a is not equal to 0 ax + b < 0 ax + b > 0

### compound inequality/sentence

consists of two simple inequalities joined by 'and' or 'or'

### equivalent inequalities

to solve a linear inequality in one variable, you isolate the variable using transformation

### absolute value

l x l the distance the number is from 0 on the number line

### extraneous solution

an apparent solution that must be rejected because it doe nor satisfy the original equation

### reflexive

looks exactily the same on both sides. (a=a)

### symmetric

a = b, b = a, having similarity in size, shape, and relative position of corresponding parts

a + b = b + a (addition), changing the order of numbers doesn't change the sum for addition or multiplication only

doughnut shape

### distributive

a ( b + c ) = ab + ac; separate into portions

### closure

a + b is a real number, any number that can be shown on a number line

### associative

( a + b ) + c = a + ( b + c , changing the grouping of numbers doesn't change the sum)

### identity

a + 0 = a, 0 + a = a, a number that combines with another number in any order without changing the original number, for addition it's 0, for multiplication it's 1

### inverse

a + (-a) = 0, additive inverse (7 + -7) and multiplicative ( 7 • 1/7)

### real number

any number that can be shown on the number line