Chapter 3.1 – 3.4 Vocabulary
Inverse Operations: two operations that undo each other, such as addition and
subtraction.
Equivalent equations: When you perform the same inverse operation on each side of
an equation; equations that have the same solution(s).
Reciprocal: A non-zero number related to another number so that their product equals
one; also called multiplicative inverse.
Terms: The parts of an expression that are added together.
Coefficients: the number part of a term with a variable part.
Constant term: a number part of an equation or expression but no variable part.
Like Terms: terms of an equation or expression that have the same
Input: Part of a function called the Domain.
Output: Part of a function called the Range.
Properties:
Addition Property of Equality: Adding the same number to both sides of the equation
Subtraction property of Equality: Subtracting the same number to each side of an
equation produces an equivalent equation.
Multiplication property of equation: multiplying each side of an equation by the same
non-zero number produces an equivalent equation.
Division Property of Equality: dividing each side of an equation by the same nonzero number produces an equivalent equation.
Distributive Property: Finding the product of a number and a sum or difference; ex.
3(x + 2) = 3(x) + 3(2)
Equivalent Expressions: Two expressions that have the same value for all values of
the variable.
Reciprocals: two numbers whose product is 1.
To solve equations with variables on both sides, collect the variable terms on one
side of the equation and the constant terms on the other side of the equation.
Number of Solutions: Equations do not always have one solutions. An equation that
is true for all values of the variable is an identity equation..
ex. 2x + 10 = 2(x + 5)
3(2a + 2) = 2(3a + 3)
For an equation that has no solution, write No Solution.
ex. 9z + 12 = 9(z + 3)