Ch 6 Sec 1: Slide #1 Columbus State Community College Chapter 6 Section 1 The Addition Property of Equality

Ch 6 Sec 1: Slide #2 The Addition Property of Equality 1.Use the addition property of equality. 2.Simplify equations, and then use the addition property of equality.

Ch 6 Sec 1: Slide #3 Addition Property of Equality (Reminder) Addition Property of Equality If a = b, then a + c = b + c and a – c = b – c. In other words: We can add the same number to both sides of an equation without changing the solution. We can subtract the same number from both sides of an equation without changing the solution.

Ch 6 Sec 1: Slide # Variable Terms on Both Sides of an Equation EXAMPLE 1 Variable Terms on Both Sides of an Equation Solve. 3 4 n +8=33– n n n n +8= – n = n =

Ch 6 Sec 1: Slide # Variable Terms on Both Sides of an Equation EXAMPLE 1 Variable Terms on Both Sides of an Equation Solve.Check 3 4 n +8=33– n ( 20 ) +8= 33 – ( 20 ) = 33 – 1 2 = – 10 = 23Balances

Ch 6 Sec 1: Slide #6 Variable Terms on Both Sides of an Equation EXAMPLE 2 Variable Terms on Both Sides of an Equation Solve. 1 4 p –3= p 5 4 – p 1 4 – p 1 4 p =– 3 –3= p 4 4

Ch 6 Sec 1: Slide #7 Variable Terms on Both Sides of an Equation EXAMPLE 2 Variable Terms on Both Sides of an Equation Solve.Check 1 4 p –3= p –3 3 1 – = – –3 3 4 – – 3 4 – 12 4 – 15 4 = – 4 = – 4 = – 4 Balances

Ch 6 Sec 1: Slide #8 – x– x Rule for – x If a is a number and – x = a, then x = – a.

Ch 6 Sec 1: Slide #9 Simplifying an Equation before Solving EXAMPLE 3 Simplifying an Equation before Solving Solve7m + 15 – 2m = 6 + 3m – 23. 5m + 15=3m – 17 – 3m 2m + 15=– 17 – 15 2m2m=– m=– 16

Ch 6 Sec 1: Slide #10 Simplifying an Equation before Solving EXAMPLE 3 Simplifying an Equation before Solving Check Solve7m + 15 – 2m = 6 + 3m – ( – 16 ) + 15 – 2 ( – 16 )= ( – 16 ) – 23 ( – 112 ) + 15 – ( – 32 ) ( – 112 ) – – 65 = 6 + ( – 48 ) – 23 = – 42 – 23 = – 65 Balances

Ch 6 Sec 1: Slide #11 Using the Distributive Property to Simplify an Equation before Solving EXAMPLE 4 Simplifying an Equation before Solving Solve3 ( x – 7 ) – ( 6 – 5x ) = ( x – 7 ) – 1 ( 6 – 5x ) = 45 3 ( x )– 3 ( 7 )– 1 ( – 5x )– 1 ( 6 )= 45 3x – 21 – 6 + 5x = 45 8x – 27 = 45

Ch 6 Sec 1: Slide #12 Using the Distributive Property to Simplify an Equation before Solving EXAMPLE 4 Simplifying an Equation before Solving Solve3 ( x – 7 ) – ( 6 – 5x ) = x – 27 = 72 8x – 27 = 9 8x – 27 = 45

Ch 6 Sec 1: Slide #13 Using the Distributive Property to Simplify an Equation before Solving EXAMPLE 4 Simplifying an Equation before Solving Solve3 ( x – 7 ) – ( 6 – 5x ) = 45.Check 3 ( 9 – 7 ) – 1 ( 6 – 5 9 )= 45 3 ( 2 ) – 1 ( 6 – 45 ) 6 – 1 ( – 39 ) = 45 Balances

Ch 6 Sec 1: Slide #14 The Addition Property of Equality Chapter 6 Section 1 – Completed Written by John T. Wallace