2-3: Solving Multi-Step Equations Essential Skills: Solve equations involving more than one operation Solve equations involving consecutive integers

2-3: Multi-Step Equations Example 1A: Solve 2q + 11 = 3. Solve using PEMDAS, backwards 2q + 11 = 3 Original equation 2q + 11 – 11 = 3 – 11 Subtract 11 from each side 2q = -8 2q/2 = -8/2 Divide each side by 2 q = -4

2-3: Multi-Step Equations Example 1B: Solve Original equation Multiply each side by 12 k + 9 = -24 k + 9 – 9 = -24 – 9 Subtract 9 from each side k = -33

1) Solve 6v + 7 = -5 v = -2 v = -6 v = 2 v = 1/3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

2) Solve j = 17 j = -17 j = 19 j = -19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

2-3: Multi-Step Equations Example 2: Write an equation and solve the problem Fourteen less than three fourths of a number is negative eight. Find the number. ¾n – 14 = -8 Translate to English ¾n – 14 + 14 = -8 + 14 Add 14 to each side ¾n = 6 4/3 ● ¾n = 4/3 ● 6 Multiply each side by 4/3 n = 8

3) Three-fourths of the difference of a number 3) Three-fourths of the difference of a number and 7 is negative fifteen. What is the number? -13 -15 ¾ 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

2-3: Multi-Step Equations Consecutive Integers Integers that come in counting order Symbols: n, n + 1, n + 2, … Example: …, -2, -1, 0, 1, 2, … Consecutive Even Integers Even integers followed by the next even integer Symbols: n, n + 2, n + 4, … Example: …, -2, 0, 2, 4 … Consecutive Odd Integers Odd integers followed by the next odd integer Example: …, -1, 1, 3, 5, …

2-3: Multi-Step Equations Example 3: Write an equation for the problem below. Then solve the equation and answer the problem. Find three consecutive odd integers whose sum is 57. Let n = the first odd integer Let n + 2 = the second odd integer Let n + 4 = the third odd integer The sum of three consecutive odd integers is 57 n + (n + 2) + (n + 4) = 57 3n + 6 = 57 Combine like terms 3n + 6 – 6 = 57 – 6 Subtract 6 from each side 3n = 51 3n/3 = 51/3 Divide each side by 3 n = 17

2-3: Multi-Step Equations Example 3 (continued) The sum of three consecutive odd integers is 57 n + (n + 2) + (n + 4) = 57 3n + 6 = 57 Combine like terms 3n + 6 – 6 = 57 – 6 Subtract 6 from each side 3n = 51 3n/3 = 51/3 Divide each side by 3 n = 17 17 is the first integer 17 + 2 = 19 is the second integer 17 + 4 = 21 is the third integer

4) Find three consecutive even integers whose sum is 84. 28, 30, 32 26, 28, 30 20, 20, 24 40, 20, 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

2-3: Multi-Step Equations Assignment Page 93-94 1 – 29 (odds) Must show work for credit