Solving Equations With Multiplication and Division

Properties

Solve. Then check your solution. Example 3-1a Answer: Multiply each side by 12.

Solve. Example 3-1b Answer: 12

Solve. Then check your solution. Example 3-2a Original equation Rewrite each mixed number as in improper fraction. Multiply each side by, the reciprocal of.

To check that is the solution, substitute for k in the original equation. Example 3-2b Answer: or Check this result.

Example 3-2c Solve. Answer:

Solve. Example 3-3a To check that 5 is the solution, substitute 5 for b in the original equation. Original equation Answer: Check this result. Multiply each side by, the reciprocal of –15.

Solve. Example 3-3b Answer:

Solve. Then check your solution. Example 3-5a Original equation Answer: and To check, substitute 13 for w. Divide each side by 11.

Solve. Then check your solution. Check: Answer: 17 Example 3-5b

Solve. Example 3-6a Original equation and Answer: Divide each side by –8.

Solve. Example 3-6b Answer: –23

Example 3-7a Write an equation for the problem below. Then solve the equation. Negative fourteen times a number equals 224. Original equation Answer: Check this result. Negative fourteen times a number equals 224. n–14224 Divide each side by –14.

Negative thirty-four times a number equals 578. Find the number. Example 3-7b Answer: –17

Multi-Step Equations

Review - Practice What to add to BOTH sides to solve for x x – 9 = x = = x – ( - x ) = 88 x – ( - 52 ) = - 36

Review - Practice What to add to BOTH sides to solve for x x – © = 10 13,000 + x = 0 12 = x + ¼ – ( - x ) = 100,000,000

Solving Multi-Step Problems Goal – To get the variable by itself Process – Combine terms and undo processes until variable is alone Undoing processes requires PEMDAS in reverse

Solve. Then check your solution. Example 4-2a 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.

Solve. Example 4-2b Answer: 14

Homework Quiz

Group Work

Example

Group Work Divide pennies into two equal piles Put the same number of pennies under each of several cups Write out the equation represented Switch tables to solve another groups problem, calculating the number of pennies under a cup.

Solve. Then check your solution. Example 4-3a Simplify. Original equation Answer: s = –240 Simplify. Multiply each side by 12. Subtract 9 from each side.

Example 4-3b To check, substitute –240 for s in the original equation.

Solve. Example 4-3c Answer: 363

Solve. Example 4-4a Original equation Simplify. Answer: r = 14 Simplify. Multiply each side by –3. Add 8 to each side.

Example 4-4b Solve. Answer: 21

Review - Practice How to solve for x 8x = = 86x

Review - Practice How to solve for x -5.73x = x = 6.272

Example 4-5a Write an equation for the problem below. Then solve the equation. 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.

Example 4-5b Simplify. Answer: n = –14 Multiply each side by.

Example 4-5c Three-fourths of seven subtracted from a number is negative fifteen. What is the number? Answer: –13

Example 4-6a 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 4-6b Simplify. Original equation Simplify. or 19 or 21 Answer: The consecutive odd integers are 17, 19, and 21. Subtract 6 from each side. Divide each side by 3.

Example 4-6c Find three consecutive even integers whose sum is 84. Answer: 26, 28, 30

Example 4-1a 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 4-1b 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 4-1c Olivia went to the mall to spend some of her monthly allowance. She put $10 away so it could be deposited in the savings account at a later date. The first thing she bought was a CD for $ The next stop was to buy hand lotion and a candle, which set her back $9.59. For lunch, she spent half of the remaining cash. She went to the arcade room and spent $5.00 and took home $1.21. How much was Olivia’s monthly allowance? Answer: $48.00

Homework Write this in your planner Evens All