Download 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:
Subtraction Property
Addition Property
 X–6
= 10
 X – 6 + 6 = 10 + 6
 X
= 16
 Y+4
 Check:
 Check:
 X – 6 = 10
 Y+4 =9
 16 – 6 = 10
 5+4 =9


10 = 10
 RIGHT ANSWER!!!!!
=9
 Y+4 -4 =9–4
 Y
=5
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
 2x
 Check:
 Check:
 -c/6
 2x
=5
 -(-30)/6 = 5
 30/6
=5
 5
=5
= 16
 2x/2 = 16/2
 X
= 8
= 16
 2(8) = 16
 16 = 16
Check Understanding:
 Solve: (Hint:
B
 AB = BC)

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