Download The Addition and Multiplication Properties of Equality

Section 2.2
The Addition and Multiplication Properties of Equality
Linear Equations in One Variable: contain one variable with no exponents
3x + 12 = 18 is a linear equation
x2 + y2 = 16 is not a linear equation
Isolating the variable: The goal is to get the variable alone on one side of the =
Equivalent equations: equations that have the same solution
Addition Property of Equality: You can add the same thing (positive or negative) to
both sides of an equation.
Transforming equations:
“Hop and Swap” If you move something across the equal sign it changes its sign.
x + 8 = 12
transforms to
x = 12 – 8
Multiplication Property of Equality: You can multiply (or divide) both sides of an
equation by the same thing – but you can’t divide by zero!
Symmetric Property of Equality:
8=x
is the same as x = 8
Always solve for the positive variable: Change
by multiplying both sides of the equation by – 1
–x=5
to
x=–5
Fractions in equations: Any time you have both a fraction and an equal sign multiply
both sides of the equation by the LCD.
x
6
5
multiply by 5
x = 30
1
x4
6
multiply by 6
x = 24
Order of Operations:
1)
2)
3)
4)
Clean up each side of the equation by simplifying the expression on that side
Move the variables first – move the small one over by the big one
Move the numbers the opposite way.
The last thing that you do when solving most equations is to divide by the
number that is connected to the variable by multiplication