Lesson 3-4 Solving Multi-Step Equations

Objectives Solve problems by working backward Solve equations involving more than one operation

Vocabulary Work backward – undoing operations of equations Multi-step equations – equations involving more than one operation Consecutive integers – integers in counting order Number theory – the study of numbers and the relationships between them

Working Backward Start with the answer “Undo” the operation that got you to the answer Keep “undoing” until you get back to the beginning

Example 1 Danny took some rope with him on his camping trip. He used 32 feet of rope to tie his canoe to a log on the shore. The next night, he used half of the remaining rope to secure his tent during a thunderstorm. On the last day, he used 7 feet as a fish stringer to keep the fish that he caught. After the camping trip, he had 9 feet left. How much rope did he have at the beginning of the camping trip?

Example 1 cont Start at the end of the problem and undo each step. StatementUndo the Statement He had 9 feet left. He used 7 feet as a fish stringer. He used half of the remaining rope to secure his tent. He used 32 feet to tie his canoe =  2 = = 64 Answer:He had 64 feet of rope. Check the answer in the context of the problem.

Example 2 Solve. Then check your solution. Simplify. Answer: Simplify. To check, substitute 10 for q in the original equation. Original equation Add 13 to each side. Divide each side by 5.

Example 3 Solve. Then check your solution. Simplify. Original equation Answer: s = –240 Simplify. Multiply each side by 12. Subtract 9 from each side.

Example 4 Write an equation for the problem and solve. Eight more than five times a number is negative 62. Original equation Simplify. Eight more than five times a number is negative 62. n Subtract 8 from each side. Simplify. Answer: n = –14 Multiply each side by.

Example 5 Number Theory 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 least odd integer. Let n + 2 = the next greater odd integer. Let n + 4 = the greatest of the three odd integers. The sum of three consecutive odd integers is 57. =57

Example 5 (cont) Simplify. Subtract 6 from each side. Divide each side by 3. Answer: The consecutive odd integers are 17, 19, and 21. Original equation

Summary & Homework Summary: –Multi-step equations can be solved by undoing the operations in reverse of the order of operations Homework: –pg 145-6; even