© William James Calhoun, : Solving Multi-Step Equations OBJECTIVES: You will be able to solve problems by working backwards, and solve equations involving more than one operation. Working backwards is one problem-solving strategy that can be employed to solve problem. It can also help with homework problems. If you can not get to the answer from the problem by yourself, you might can work from the answer to the problem to learn how to do similar problems. EXAMPLE 1: Due to melting, an ice sculpture loses one-half its weight every hour. After 8 hours, it weighs 5 / 16 of a pound. How much did it weight in the beginning? Work backwards. Now4hr ago8hr ago 1hr ago5hr ago 2hr ago6hr ago 3hr ago7hr ago 5 / 16 5/85/8 5/45/4 5/25/ lbs. Double the weight each hour backward.

© William James Calhoun, 2001 ( ) 3( )3 ( ) 5( )5 3-3: Solving Multi-Step Equations EXAMPLE 3: Solve each equation. A.B. What is on the same side as y? 5 and 9 Which is farther from y? 9 How is 9 combined with y? added 9 To undo add nine… Subtract 9 from both sides. What is on the same side as d? 2 and 3 Which is farther from y? 3 How is 3 combined with y? divided by 3 To undo divide by three… Multiply by 3 on both sides. Cancel and multiply How are y and 5 combined? divided by 5 To undo divide by 5… Multiply both sides by 5. Cancel and multiply. 1 1 y = -15 d - 2 = 21 How are d and 2 combined? subtracted 2 To undo subtract 2… Add 2 to both sides. +2 d = 23 Write the equation.

© William James Calhoun, : Solving Multi-Step Equations 3b = -51 A quick helpful hint for SOME problems. You can use it here.You can not use it here. 1(3b + 1)=2(-25) 3b + 1 = b = -17 You can cross multiply to solve equations - only when you have fraction = fraction.

© William James Calhoun, : Solving Multi-Step Equations EXAMPLE 4: Find three consecutive odd integers whose sum is -15. Even though we only dealt with consecutive odd integers in our example and practice, the way we set up the problems works for consecutive even integers as well. If a problem asks for “consecutive integers”, that would be like 2, 3, 4, etc. In that case, the first integer would be “n”, the second “n + 1”, third “n + 2”, etc. So for consecutive, add one each step. For consecutive odd or even integers, add two each step. On the consecutive problems, use a chart. 1st 2nd 3rd n n + 2 n + 4 Sum means add, so add the numbers down the column. 3n + 6 This must equal -15 from the problem. 3n + 6 = -15 Solve this equation to find the first number. -6 3n = n = -7 This is the first number. Use the chart to get the other two

© William James Calhoun, : Solving Multi-Step Equations HOMEWORK Page 160 # odd