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Solve/Justify Linear

Solve and Justify Linear Equations

TermDefinition
Associative Property The way in which numbers are grouped does not change their sum (adding) or product (multiplying). 2+(5+6) = (2+5)+6 OR 2x(5x6) = (2x5)x6
Commutative Property The order in which numbers are added or multiplied does not change the sum or product. 2+7 = 7+2 OR 2x7 = 7x2
Additive Identity Property The sum of any number and zero is the number (3+0=3)
Additive Inverse Property The sum of a number and its opposite is zero. 15 + (-15) = 0 or (-15) + 15 = 0
Multiplicative Identity Property The product of any number and one is the number. 9x1 = 9
Multiplicative Inverse Property The product of a nonzero number and its reciprocal is one. 3x(1/3) = 1
Distributive Property When multiplying a number by a sum OR difference, the number can be multiplied by each term in the sum OR difference. 4x(6-8) = 4x6 - 4x8
Like Terms Terms that contain the same variables raised to the same power. Example: 4x & 6x are like terms. 5 & 8x are NOT like terms.
Opposite Operations Operations that "undo" one another. Addition and subtraction are opposite operations. Multiplication and division (sometimes shown as fractions) are opposite operations. Exponents and radicals (or roots) are opposite operations.
How do you keep an equation balanced? By performing the same operation to both sides of the equals sign.
What property would you need to use FIRST to solve the equation: 12-2(2-x) = 4(x+3)-7x Distributive Property
What step would you need to take to continue solving this equation: 12-4+2x = 4x+12-7x Combine Like Terms
What property would you need to use to continue solving this equation: 5x = 12 Division Property of Equality
What is the solution to this equation? -3x-7 = 2x+23 x = -6
Created by: zoe73189
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