Solving Equations With Multiplication and Division Properties Solve

Solving Equations With Multiplication and Division

Properties

Solve. Then check your solution. Multiply each side by 12. Answer:

Solve Answer: 12 .

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

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

Solve Answer: .

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

Solve Answer: .

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

Solve Answer: 17 Check: . Then check your solution.

Solve . Original equation Divide each side by – 8. Answer: and

Solve Answer: – 23 .

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

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

Multi-Step Equations

Review - Practice • What to add to BOTH sides to solve for x x – 9 = 10 13 + x = 25 14 = x + 20 124 – ( - 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 - 124 – ( - x ) = 100, 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. Original equation Add 13 to each side. Simplify. Divide each side by 5. Answer: Simplify. To check, substitute 10 for q in the original equation.

Solve Answer: 14 .

Homework Quiz

Group Work

Example

Example

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. Original equation Subtract 9 from each side. Simplify. Multiply each side by 12. Answer: s = – 240 Simplify.

To check, substitute – 240 for s in the original equation.

Solve Answer: 363 .

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

Solve Answer: 21 .

Review - Practice • How to solve for x 8 x = 48 -1634 = 86 x

Review - Practice • How to solve for x -5. 73 x = 97. 41 0. 49 x = 6. 272

Write an equation for the problem below. Then solve the equation. Eight more than five times a number is negative 62. Eight 8 more than five 5 times a number is negative 62. n 62 Original equation Subtract 8 from each side. Simplify.

Multiply each side by Answer: n = – 14 Simplify. .

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

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

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

Find three consecutive even integers whose sum is 84. Answer: 26, 28, 30

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?

Start at the end of the problem and undo each step. Statement Undo the Statement 9 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. 9 + 7 = 16 16 2 = 32 32 + 32 = 64 Answer: He had 64 feet of rope. Check the answer in the context of the problem.

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 $15. 99. 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 • 3 -3 - Evens • 3 -4 - All