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Elementary Algebra Notes
Section 2.1
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Section 2.1: The Additive Property of Equality
Big Idea:
An equation is when two algebraic expressions are set equal to each other.
An algebraic expression represents a multi-step calculation, so setting it equal to something means you know
what you want the answer to be, but you don’t know what number to put in for your variable to get that answer
you want.
Finding that number is called “solving” the equation.
Solving an equation involves “undoing” the calculation represented by the expression to expose the variable.
To “undo” an expression, you must do the opposite of the order of operations. That is to say, you start with
adding or subtracting.
Big Skill: You should be able to solve simple equations using the addition property of equality, and then check
your solution.
Definition: Linear Equation in One Variable
A linear equation in one variable can be written in the form
Ax + B = C
For real numbers A, B, and C, and C  0.
The addition property of equality: The same number may be added to (or subtracted from) each side of an
equation without changing the equation. Algebraic statement:
If
then
A = B,
A + C = B + C.
Practice: Solve the following equations, then check your work.
1. x – 3 = 10
2. m + 7 = 5
3. 2y + 12 – y + 10 = 22
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.
Elementary Algebra Notes
Section 2.1
Page 2 of 2
4. 3x + 4 + 5x + 6 = 10x + 15 – 3x
5.
7
9
k 1  k  5
2
2
6. 4  z  1   3z  5  1
Strategies to note from above:
 Sometimes you need to simplify both sides (by combining like terms or removing parentheses using
distribution) before you can use the addition property of equality.

Sometimes you need to add or subtract terms with variables from both sides.
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.