1. Problems to be Done! 2 – Addition 2 – Subtraction 2 – Multiplication 2 – Division 2 – Distributive 2 – Special Solution 1 – Multi-Step Word Problem 2 – Write and Solve 3 – Solve and Graph

2. Addition Property of Equality If an equation is true and the same number is added to each side of the equation, the resulting equivalent equation is also true. For any real numbers a, b, and c, the following is true. – 1) If a = b, then a + c = b + c

3. Addition Property of Equality x – 12 = 8Original Equation x – 12 + 12 = 8 + 12Add 12 to each side x = 20 Simplifying Try These: 1) 22 = m – 82) d – 14 = -19

4. Subtraction Property of Equality If an equation is true and the same number is subtracted from each side of the equation, the resulting equivalent equation is also true. For any real numbers a, b, and c, the following is true. – 1) If a = b, then a - c = b - c

5. M + 19 = 56Original Equation M + 19 – 19 = 56 – 19Subtract 19 from both sides M = 37Simplify – 1) x + 23 = 142) p + 8 = 18 Subtraction Property of Equality

6. Multiplication Property of Equality If an equation is true and each side is multiplied by the same nonzero number, the resulting equation is equivalent. For any real numbers a, b, and c, c ≠ 0, – if a = b then ac = bc – Example: If x = 5, then 3x = 15

7. Multiplication Property of Equality Of the students surveyed at Madison High School, eighty-four said they have never purchased an item online. This is about one eighth of those surveyed. How many students were surveyed? – 1n/8 = 84Original Equation – (8) 1n/8 = 84(8)Multiply each side by 8 – n = 672Simplify

8. Multiplication Property of Equality Examples: 1.) - 3r/7 = 212.) -4p/3 = -10

9. Division Property of Equality If an equation is true and each side is divided by the same nonzero number, the resulting equation is equivalent. For any real numbers a, b, and c, c ≠ 0, – if a = b then a/c = b/c – Example: If x = -20, then x/5 = -20/5

10. Division Property of Equality 39 = -3rOriginal Equation 39/-3 = -3r/-3Divide each side by -3 -13 = rcheck the result Examples 1. -75 = -15b 2. 12t = - 132

11. Distributive Property Equality ExampleSteps Done 4(3t – 5) + 7 = 8t + 3 Original Equation 12t – 20 + 7= 8t + 3Distributive Property 12t – 13 = 8t + 3Combine Like terms 4t – 13 = 3Subtract 8t from each side 4t = 16Add 13 to each side 4t/4 = 16/4Divide 4 from both sides T = 4Simplify

12. Distributive Property 1) 6(5z – 3) = 36z2) 2(h+6) = -3(8-h)

13. Special Solutions 9t – 5(t-5) = 4(t-3)Original Equation 9t – 5t + 25 = 4t – 12Distributive Property 4t + 25 = 4t – 12 Combine Like Terms 4t + 25 – 4t = 4t – 12 – 4t Subtract 4t from both sides 25 = 12Simplify If the equation is not True then the answer is NO SOLUTION!

14. Special Solutions 3(4m + 6) = 42 + 6(2m -4) 12m + 18 = 42 + 12m – 24Distributive 12m + 18 = 12m + 18Combine Like Terms 12m+18–12m = 12m + 18 – 12m Subtract 12m 18 = 18Simplify When your equation ends up true like this the answer is All Real Numbers!

15. Special Solutions 1) 18 – 3(8c + 4) = -6(4c – 1) 2) 46 = 8m – 4(2m + 5)

16. Multi-Step Equation Write and solve an equation to find the sales Mrs. Jones needs if she earns a monthly salary of $2,000 plus a 10% commission on her sales. Her goal is to make $4,000 per month. What sales does she need to make her goal?

17. Write and Solve the Equation Seventeen is thirteen subtracted from six times a number. What is the number? Fourteen less than three fourths of a number is negative eight. Find the number.

18. Solve and Graph

19. Answers Addition: 1) m = 302) d = -5 Subtraction: 1) x = -92) p = 10 Multiplication: 1) r = -492) p = 7 and ½ Division: 1) 52) -11 Distributive: 1) z = -3 2) h = 36 Special Solutions: 1) Real Numbers2) No solution Multi-Step 1) x = 20,000 Write & Solve: 1) 17 = 6x -13; n = 8 2) n=5; 3n/4 -14=-8 Solve and Graph: 1) x = 82) x = 6 – 3) x = 88