Four Basic Rules for Solving an Equation.pptx

Basic rules for Solving an Equation

1. 2a + 7 a 7 2 x - 3 x -3 1 3y - 7 y -7 3 3a + 16 a 16 3 2n - 9 n - 9 2

2. The Four Basic Rules for Solving an Equation 1. Addition Property of Equality If the same quantity is added to both sides of an equation, the resulting equation is equivalent to the original equation. Example: x–6=16 add ( +6 ) to both sides x–6 +6 = 16 +6 x = 22 -6+6=0 16+6=22

3. x-3 = 7 y−5 =10 a-4 =12 x-2 = 10 z-6 = 7

4. 2. Subtraction Property of Equality If the same quantity is subtracted from both sides, the resulting equation is equivalent to the original. Example: x + 6= 16 subtract both sides by ( -6 ) x+6 –6 = 16 -6 x = 10 6-6=0 16-6=10

5. x+5 = 10 y+3 = 8 x+6 = 15 z+8 = 10 a+5 = 20

6. 3. Multiplication Property of Equality If both sides of an equation are multiplied by the same (nonzero) quantity, the resulting equation is equivalent to the original equation. Example: = 15 multiply both sides by 5 5 = 15 5   15x5 =75 5 is cancelled out X = 75

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8. 4. Division Property of Equality If both sides of an equation are divided by the same (nonzero) quantity, the resulting equation is equivalent to the original equation. Example: 5x =15 divide both sides by 5 =   X = 3

9. 5x = 25 12y = 48 − 6z = 42 3a = −21 − 8b = −64

10. Let’s try to translate and solve the following equation: I am six years older than twice the age of my youngest sister. If I were 66 years old. How old is my youngest sister? Twice the age ( 2n ) + six years older (+6) = 66 years old 2n + 6 = 66

11. Let’s try to translate and solve the following equation: I am six years older than twice the age of my youngest sister. If I were 66 years old. How old is my youngest sister? Twice the age ( 2n ) + six years older (+6) = 66 years old 2n + 6 = 66 2n + 6 – 6 = 66 -6 (Subtraction Property of Equality) -6 2n = 60 2 2 (Division Property of Equality) /2 N = 30

12. 2x + 4 = 16 68 = 3y – 4 3. = 17   4. = 7 5. 5y + 0 = 125   Solve the following equation using the 4 basic rule in solving equation.

13. 1. I am 24 years old. My age is 2 less than twice my sister’s age. 2. Arvin has a bake shop. He sold 85 cakes today. That is 16 cakes fewer than yesterday. How many cakes did he sell yesterday? 3. Ann have 56 stamps that are 6 less than one-half of my stamps. How many stamps do I have? Translate each problem into a mathematical equation then solve: