Algebra 1: Module 1: 01.07 Algebraic Properties and Equations

Steps to Solving an Equation

1.)Use the distributive property to remove parenthesis if they exist in the equation. 2.)Combine like terms on both sides of the equation Read the equation and decide what operations (add, subtract, multiply, divide) are being applied to the variable. 3.)Use the algebraic properties to undo each of these operations one at a time. 4.)You are finished when the variable is isolated on one side of the equation by itself. 5.)Check your solution by substituting it into the original equation and testing to see whether it gives you a true equation

Distributive Property

States that any number multiplied to a sum or difference of two or more numbers is equal to the sum or difference of the products. ~3(5 + 2) = 3(5) + 3(2) ~2(6 − 8) = 2(6) − 2(8)

Associative Property

States that grouping symbols does not affect the outcome. This property works for Addition and Multiplication. ~2 + (3 + 4) = (2 + 3) + 4 ~6 • (5 • 4) = (6 • 5) • 4

Commutative Property

States that the order in which you perform an operation does not affect the outcome. This property works for Addition and Multiplication. ~5 + 4 = 4 + 5 ~2 • 3 = 3 • 2

Properties of Equality

~Reflexive Property says that anything is equal to itself. −2 = −2 ~Symmetric Property says that the order on either side of the equal sign does not matter. a = 6 is the same as 6 = a ~Transitive Property says for any real numbers a, b, and c if a = b, and b = c, then a = c. 1 + 6 = 7 and 7 = 3 + 4 then 1 + 6 = 3 + 4 ~Addition Property says if a = b, then a + c = b + c. ~Subtraction Property says if a = b, then a − c = b − c. ~Multiplication Property says if a = b, then a • c = b • c. ~Division Property says if a = b, then a/c = b/c. ~Substitution Property says if a = b, then b can replace a in any expression without changing the value of the expression.

Other Helpful Tips

~When dividing or multiplying by negatives, be careful with your signs. Remember, two negatives multiplied or divided make a positive answer. Multiplying or dividing a negative and a positive will make a negative answer. (−2)(−3) = +6, (2)(−3) = −6 ~When dealing with a negative in front of a fraction, write the negative with the numerator and leave the denominator positive. If you were to write negatives in both the numerator and the denominator, you would create a positive value. The number −(1/2) is the same as −1/2. The number −1/−2 is the same thing as positive 1/2. ~Work with the fraction to clear the denominator. Multiply all terms on both sides by the denominator.