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3.1: One-Step Equations and Inverse Operations

Difficulty Level: Basic Created by: CK-12
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Vocabulary

Addition Property of Equality

For all real numbers a, b, and c: If a = b, then a + c = b + c.

equivalent equation

By applying the same inverse operations to each side of an equation, you create an equivalent equation. Equivalent equations are two or more equations having the same solution.

inverse operation

Each of these operations has an inverse. Inverse operations undo each other when combined.

Multiplication Property of Equality

For all real numbers a, b, and c: If a = b, then a(c)= b(c).

one-step equations

Equations that take one step to isolate the variable. Such equations can also involve multiplication or division.

solving equations

To solve an equation means to write an equivalent equation that has the variable by itself on one side. This is also known as isolating the variable.

constant

A constant is a value that does not change. In Algebra, this is a number such as 3, 12, 342, etc., as opposed to a variable such as x, y or a.

Equation

An equation is a mathematical sentence that describes two equal quantities. Equations contain equals signs.

Numerical Coefficient

In mathematical expressions, the numerical coefficients are the numbers associated with the variables. For example, in the expression 4x, 4 is the numerical coefficient and x is the variable.

Variable

A variable is a symbol used to represent an unknown or changing quantity. The most common variables are a, b, x, y, m, and n.

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MAT.ALG.220.L.1