Unit 5 inequalities and equations

Multiplication Property of Equality

States that if each side of an equation is multiplied by the same nonzero number, the two sides remain equal and the resulting equivalent equation is true. Ex: 2x=4, then 2x 1 = 4 1 2 2

Multiplicative Property of Zero

When you multiply any Number by 0 you get 0. Ex: 8 x0= 0

Identity Elements

are numbers that combine with other numbers without changing the other numbers. The additive identity is zero (0) Ex: 5 +0=5 . The multiplicative identity is one (1). Ex: 8x1 =8

Linear Equation

is an equation in which the variables are raised to the first power. A linear may have one variable or several variables. An equation is one variable can be of the form ax + b=0 where x is the variable , a is the numerical coefficient, and b is the constant.

Linear Inequality

is one variable can be of the form ax +b > 0 or 0 < ax + b where x is the variable.

Identity Property of Multiplication

multiply by 1 to any number and get the same number. Example: 8 x1= 8

Subtraction Property of Equality

states that is the same number added is subtracted from each side of the equation, the two sides remain equal and the resulting equivalent equation is true. Ex: x +2= 4 , then x+2 -2= 4-2

Like Terms

to combine terms that have the same variable and the same exponent. Example: 8x +11 -3x can be 5x +11.

Inverse Property of Multiplication

when you multiply a number and its reciprocal always equals 1. Example: 4 x 1 = 1 4