Replacing a variable with a number to solve an equation.
Equations that have the same solution.
addition property of equality (EOA)
Adding the same amount to both sides of an equation to keep it equal.
subtraction property of equality (EOS)
Subtracting the same amount from both sides of an equation to keep it equal.
multiplication property of equality (EOM)
Multiplying the same amount to both sides of an equation to keep it equal.
division property of equality (EOD)
Dividing the same amount to both sides of an equation to keep it equal.
solving for the variable
Using equality properties to simplify an equation to the point of finding the value or values of the variable that make the equation true.
isolating the variable
Using equality properties to isolate the variable to one side of the equation.
Terms that are only constants or are terms with variables that are identical. For example x^2y is a like term to -5x^2y, but is not a like term to 2xy. The x is not squared in 2xy, so the variables in the terms are not considered alike.
combining like terms
Simplifying like terms by combining their coefficients.
multiplicative inverse (reciprocal)
The flip side of a fraction or of a number written in fraction form. Example, the M.I. to 3 is 1/3 and the M.I. to -4/3 is -3/4. When multiplied, their solution is 1.
Adding a negative number is the same as subtracting the positive of that number.
Subtracting a negative number is the same as adding the positive of that number (2 - (-4) = 2 + 4)
Multiplying a negative number by a positive number results in the product having a negative value. If both numbers being multiplied are negative, then their product is positive.
Dividing a negative number by a positive number results in the quotient having a negative value. If both numbers being divided are negative, then their quotient is positive.
A rectangular arrangement of numbers. The number of rows and columns determine its size. Each item in a matrix is called an element.
When one expression is less than, greater than, less than or equal to, or greater than or equal to another expression.
solving an inequality with a negative coefficient
When dividing or multiplying an entire inequality by a negative number, the inequality will flip. > will become <, and vice versa.
Two inequalities that are joined by the word "and" or the word "or".
The number that is multiplied by the variable with exponents that are whole numbers (like the 3 in 3x)
An expression that contains at least one variable.
order of operations
A rule for evaluating expressions (PEMDAS/GEMDAS).
A value that does not change.
An expression that contains only numbers and operations.
The parts of an expression that are added or subtracted.
A polynomial with two terms.
A number or a product of numbers and variables with exponents that are whole numbers.
A polynomial with three terms.
An algebraic expression that is the sum or difference of two or more monomials.
The opposite of a number.
Counting numbers starting at one.
Positive and negative whole numbers.
Counting numbers starting at zero.
The distance a number is from zero on the number line.
A mathematical sentence that shows the relationship between quantities that are not equivalent.
A mathematical sentence that shows the relationship between quantities that are equivalent.
A mathematical sentence with at least one variable that shows two expressions are equivalent.
A mathematical sentence with only numbers that shows two expressions are equivalent.
A number that exists and behaves rationally or irrationally.
A number that can't exist, such as zero to the zero power or the square root of a negative number.
A number that is multiplied by another number to get a product.
A number produced by raising a base to an exponent.
A symbol (usually a letter of the alphabet) used to represent a quantity that can change.
The number that is used as a factor when it is raised to a power.
The number that indicates how many times the base is used as a factor.
a(0) = 0 and a + -a = 0
(a+b)+c = a+(b+c) and (ab)c = a(bc)
a+b+c = b+c+a and abc = cab
a+0 = a and a(1) = a
3(a+b) = 3a + 3b (multiply what is on the outside of the parenthesis by each term inside, then lose the parenthesis)