Chpt. 1, Expressions, Equations, and Inequalities

Question 1

constant

Answer 1

A quantity whose value does not change.

Question 2

variable

Answer 2

A quantity that is capable of variation. It is indicated with a symbol, usually a letter, that represents a number or expression. Example = “x”

Question 3

numerical expression (or just expression)

Answer 3

A mathematical phrase that contains numbers and operation symbols. Example = 3 + 5

Question 4

algebraic expression (or just expression)

Answer 4

A mathematical phrase that contains one or more variables. Example = 3x +_5

Question 5

opposite

Answer 5

The opposite, or additive inverse, of any number a, is -a. the sum of opposites is zero, the additive identity.

Question 6

reciprocal

Answer 6

The reciprocal, or multiplicative inverse, of any number a is 1/a. The product of inverses is 1, the additive identity.

Question 7

commutative property of addition
commutative property of multiplication
associative property of addition

Answer 7

a + b = b + a
ab = ba
a + (b+c) = (a+b) + c

Question 8

associative property of multiplication
distributive property
additive identity property

Answer 8

a * (bc) = (ab) * c
a * (b-c) = ab - ac
a + 0 = 0 +a = a

Question 9

multiplicative identity property
additive inverse property
multiplicative inverse

Answer 9

a1 = 1a = a
a +(-a) = 0
a*(1/a) = 1

Question 10

reflexive property
symmetrical property
transitive property

Answer 10

a = a
if a = b, then b = a
if a = b, and b = c, then a = c

Question 11

substitution property
definition of subtraction
definition of division

Answer 11

if a = b, then b can replace a in any equation

a - b = a +(-b)
0/a = 0, a/a =1, a/0 = undefined

Question 12

zero product property

closure property

Answer 12

if ab = 0, then a = 0, or b = 0

if a and b are real numbers, then a +b and ab are also real numbers

Question 13

evaluate (an expression)

Answer 13

To do this, numbers must be plugged into each of the variables in the expression, and the expression must be simplified using the order of operations.

Question 14

term (of an expression)

Answer 14

This is a number, a variable, or the product of one or more numbers or variables.

Question 15

coefficient

Answer 15

The numerical factor in a term. Example is the number “3” in y = 3x.

Question 16

constant term

Answer 16

A term with no variables.

Question 17

like terms

Answer 17

Terms that have the same variables raised to the same powers.

Question 18

equation

Answer 18

A statement that two algebraic expressions are equal. You are essentially “equating” the algebraic expressions.

Question 19

solution of an equation

Answer 19

A number that makes an equation true.

Question 20

inverse operations

Answer 20

Inverse operations are operations that undo each other. If you plug the y-values of inverse operations into each other, and set them equal to each other, then simplify, you will get x = x (assuming you’re using slope-intercept form).

Question 21

identity

Answer 21

An equation that is true for every value of a variable.

Question 22

literal equation

Answer 22

An equation that uses more than one letter as a variable.

Question 23

compound inequality

Answer 23

When two or more inequalities are joined together with the word “and.” For example: -1 < x, and x < 9. Another example: x < -1 or x> 3.

Question 24

properties of inequalities

Answer 24

All the same properties that are applied to equations can also be applied to inequalities, except that when you divide by a negative number with inequalities, you must switch the direction in which the inequality symbol faces.

Question 25

absolute value

Answer 25

The absolute value of a real number x is it’s distance from zero on the number line.

Question 26

extraneous solution

Answer 26

An extraneous solution is the solution of an equation that is derived from an original equation, but that is not a solution of the original equation.