Algebra Topic 1 Review

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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


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