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

Algebra 1 ~ Chapter Solving Multi- Step Equations

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 = add/sub first!! 2x = mult/div second!! x = 4 CHECK!! 2x + 1 = 9 2(4) + 1 = = 9 9 = 9

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

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

Examples – Solve and Check!! 5.)6.)

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

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. *** = 42

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.

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.