Notes: 2.1-2.2 Solving Equations: Addition and Multiplication Principles
Definitions:
An _____________________ is a number sentence that says that the expressions on
either side of the equal sign, =, represent the same number.
Example:
Any replacement for the variable that makes an equation true is called a
______________________ of the equation. To solve an equation means to find
_____________ of its solutions.
One way to determine whether a number is a solution of an equation is to
____________________ the expression on each side of the equal sign by
substitution. If the values are the same, then the number is a solution.
Example:
The Addition Principle for Equations:
The Multiplication Principle for Equations:
Math 409
HCC
Prof. T. Garrett
Examples: Solve using the addition or multiplication principles
1. 𝑥 + 2 = 11
2. 𝑥 + 5 = −7
3. 𝑎 − 4 = 10
2
4. −6.5 = 𝑦 − 8.4
5
6. 5𝑥 = 70
5. − 3 + 𝑥 = 2
8. −𝑥 = 9
7. −4𝑥 = 92
9.
3
8
11.
Math 409
5
10.
= −4𝑥
−𝑦
9
1.16𝑦 = 9744
= 14
HCC
Prof. T. Garrett