Algebra Topic 1 Review
change the direction of the sign
"If you multiply or divide both sides of an inequality by a negative number, you change the direction of the sign."
properties of equality
"What you do to one side, you do to the other."
Expression
A mathematical phrase that contains operations, numbers, and/or variables.
Equation
A mathematical sentence that contains an equals sign.
Term
A number, a variable, or the product of a number and a variable
Order of operations
A set of rules that tells the order in which to compute.
Variable
A symbol used to represent a quantity that can change
Constant
A value that does not change
Addition Property of Equality
Adding the same number to both sides of an equation doesn't change the equality of the equation. Example: a=b so a+c=b+c.
Integer
All whole numbers (both positive and negative) and zero.
open circle
DOES NOT include that point on a number line
closed circle
DOES include that point on a number line
Division Property of Equality
Dividing the same number to both sides of an equation doesn't change the equality of the equation. Example: a=b so a/c=b/c
Substitution Property of Equality
If numbers are equal, then substituting one in for another doesn't change the equality of the equation. Example: x=5 so y=x+6 should be y=5+6
Consecutive Integers
Integers that follow each other in order
Infinitely Many Solutions
Means that any value for the variable would make the equation true
Multiplication Property of Equality
Multiplying the same number to both sides of an equation doesn't change the equality of the equation. Example: a=b so a*c=b*c
Whole Numbers
Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...
Subtraction Property of Equality
Subtracting the same number from both sides of an equation doesn't change the equality of the equation. Example: a=b so a-c=b-c
Like Terms
Terms that have the same variable raised to the same exponent
Coefficient
The number that is multiplied by the variable in an algebraic expression
Distributive Property
The product of a number and a sum is equal to the sum of the individual products of terms.
Rational Numbers
The set of all numbers that can be written as the ratio of two integers with a non-zero denominator
Irrational Numbers
The set of all numbers that cannot be expressed as the ratio of integers
Real Numbers
The set of all rational an irrational numbers
Integers
The set of numbers ...-3, -2, -1, 0, 1, 2, 3...
Natural Numbers
The set of numbers 1,2,3,4.....
inequality
a mathematical sentence that compares quantities
solution of an inequality
a value that makes the inequality true
greater than or equal to
all the numbers larger than or equal to...
greater than
all the numbers larger than...
less than or equal to
all the numbers less than or equal to...
less than
all the numbers lower than...
compound inequality
formed by joining two inequalities with "and" or "or"
No Solution
no number solves an equation
graph of an inequality
shows the solution set on a number line
solution set
the set of all solutions of an inequality
