Algebra 1 Chapter 2 1 Solving OneStep Equations

Algebra 1: Chapter 2 -1 Solving One-Step Equations

OBJECTIVES: �To solve equations using addition and subtraction �To solve equations using multiplication and division

Addition and Subtraction Properties: �Addition Property of Equality: �For every real number a, b, and c, if a = b, then a+c = b+c Example: 8 = 5 + 3, so 8 + 4 = 5 + 3 + 4 • Subtraction Property of Equality: • For every real number a, b, and c, if a=b, then a-c = b-c Example: 8 = 5 + 3, so 8 – 2 = 5 + 3 – 2.

Important Terms: �To solve an equation containing a variable, you find the value (or values) of the variable that make the equation true, called a Solution of the Equation. �Equations that have the same solution are called Equivalent Equations. �One way to solve an equation is by getting the variable on one side of the equals sign by itself by using inverse operations (operations that undo each other)

Examples: Addition Property Subtraction Property �X – 6 = 10 �X – 6 + 6 = 10 + 6 �X = 16 �Y + 4 =9 �Y + 4 - 4 = 9 – 4 �Y =5 �Check: �X – 6 = 10 � 16 – 6 = 10 � 10 = 10 �RIGHT ANSWER!!!!! �Check: �Y + 4 = 9 � 5 + 4 = 9 � 9 =9 �RIGHT ANSWER!!!!!

Multiplication and Division Properties �Multiplication Property of Equality: �For every real number a, b, and c, if a = b, then (a)(c) = (b)(c). �Example: 6/2 = 3, so (6/2) (2) = (3)(2) �Division Property of Equality: � For every real number a, b, and c, with c ≠ 0, if a = b, then a/c = b/c. � Example: 3 + 1 = 4, so (3 + 1)/2 = 4/2

Examples: Multiplication Property Division Property �-c/6 =5 �-c/6 ∙ -6 = 5 ∙ -6 �C = -30 � 2 x = 16 � 2 x/2 = 16/2 �X = 8 �Check: �-c/6 =5 �-(-30)/6 = 5 � 30/6 =5 � 5 =5 �Check: � 2 x = 16 � 2(8) = 16 � 16 = 16

Check Understanding: � Solve: (Hint: � AB = BC) � B 15 A a + 4. 2 C

Assignment: �Pg. 77: multiples of 3 #3 -18, 20 � multiples of 3 #21 -54, � 60, 63, 69, 71, 79