1. OPENER: Solve and CHECK the following equations. 1.) − 12 + a = − 362.) t – ( − 16) = 9 3.) ¼ + x = ⅔4.) +12 +12 t + 16 = 9 a = -24 -16 -16 t = -7 -¼ -¼ x = y = 25

2. Algebra 1 ~ Chapter 3 - 4 Solving Multi- Step Equations

3. Solve Multi-Step Equations To solve equations with more than one operation, often called multi-step equations, undo operations by working backwards. PEMDAS backwards SADMEP  So start with addition or subtraction  Then take care of multiplication or division  For example, 2x + 1 = 9 -1 -1 add/sub first!! 2x = 8 2 2 mult/div second!! x = 4 CHECK!! 2x + 1 = 9 2(4) + 1 = 9 8 + 1 = 9 9 = 9

4. Example – Solve and Check! 1.) 7m – 17 = 60 + 17 +17 7m = 77 7 7 m = 11 CHECK 7m – 17 = 60 7(11) – 17 = 60 77 – 17 = 60 60 = 60 2.) − 2a + 10 = 22 - 10 -10 -2a = 12 -2 -2 a = -6 CHECK -2a + 10 = 22 -2(-6) + 10 = 22 12 + 10 = 22 22 = 22

5. Example – Solve and Check each equation. 3.) -6 -6 y = -153 4.) 4x + 5 = -35 - 5 -5 4x = -40 4 4 x = -10

6. Examples – Solve and Check!! 5.)6.)

7. Writing Equations Ex. 1 – “Twelve decreased by twice a number equals -34.” 12 – 2n = -34 Ex. 2 - “Two-thirds of a number minus six is -10.” ⅔n – 6 = -10 Ex. 3 – “A number is multiplied by seven, and then the product is added to 13. The result is 55.” 7n + 13 = 55

8. Solve a Consecutive Integer Problem *** Find three consecutive integers whose sum is 42. “3 #’s in a row” Integer #1 – n Integer #2 = n + 1 Integer #3 = n + 2(n) + (n + 1) + (n + 2) = 42 3n + 3 = 42 3n = 39 n = 13 Conclusion - The three consecutive integers whose sum is 42 are 13, 14 and 15. *** 13 + 14 + 15 = 42

9. Example – Find three consecutive EVEN integers whose sum is 72. Integer #1 – n Integer #2 – n + 2 Integer #3 – n + 4 Remember we are only looking for even numbers, so every OTHER number!! (n) + (n + 2) + (n + 4) = 72 3n + 6 = 72 3n = 66 n = 22 So the three consecutive even integers are 22, 24 and 26.

10. Example – Find three consecutive ODD integers whose sum is -51. Integer #1 – n Integer #2 – n + 2 Integer #3 – n + 4 Remember we are only looking for odd numbers, so every OTHER number!! (n) + (n + 2) + (n + 4) = -51 3n + 6 = -51 3n = -57 n = -19 So the three consecutive odd integers are -19, -17 and -15.