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**More on Solving Equations**

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**Grouping Symbols on Both Sides……**

You might have to distribute before you combine like terms.

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**Solve: 2(x+5)= 3(x + 2) + x Answer: 2x + 10 = 3(x + 2) + x**

__________________ -2x + 10 = 6 -2x = -4 x = 2 2(x+5)= 3(x + 2) + x

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**Solve: 2(3x + 2) = 2(x+8) Answer: 2(3x + 2) = 2x + 16 6x + 4 = 2x + 16**

________________ 4x + 4 = 16 _________________ 4x = 12 x = 3 2(3x + 2) = 2(x+8)

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Word Problems

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**Words that tell you to add….**

Plus Increased By Sum More Than

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**Words that tell you to subtract…**

Minus Decreased By Difference Less Than

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**Multiply and Divide Words…..**

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**Write the mathematical statement for the following…..**

9 increased by 2 5 decreased by m Sum of 4 and 2x 7 less than 12 7 increased by 5 times a number 8 decreased by 3 times a number The sum of twice a number and 5 9 + 2 5 – m 4 + 2x 12 – 7 7 + 5n 8 – 3x 2y + 5

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**You Try….. The sum of 7 and 3 times a number**

4 times Harry’s age increased by 2 8 pounds less than twice wanda’s weight 7 + 3n 4h + 2 2w - 8

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Word Problems…… The $500 selling price of a TV is $70 less than 3 times the cost. Find the profit Let’s define the variables first: Let C = Cost Let P = Profit Let SP = Selling Price

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**The $500 selling price of a TV is $70 less than 3 times the cost**

The $500 selling price of a TV is $70 less than 3 times the cost. Find the profit. Think: Cost + Profit = Selling Price C P = SP We know the selling price and are looking for the profit. Somehow we need to find the cost first: 3C – 70 = $500 3C = $570 Cost = $190. We are still looking for the profit.

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**Cost + Profit = Selling Price. 190 + P = 500 P = 500 – 190 **

The $500 selling price of a TV is $70 less than 3 times the cost. Find the profit. We know that the cost = 190. Cost + Profit = Selling Price. 190 + P = 500 P = 500 – 190 Profit = $310 (This is the answer)

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You Try…… The $140 selling price of a game is $60 less than twice the cost. Find the profit.

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**The $140 selling price of a game is $60 less than twice the cost**

The $140 selling price of a game is $60 less than twice the cost. Find the profit. 1st find the cost: 2C – 60 = 140 2C = 2C = 200 C = $100 2nd find the profit: C + P = SP 100 + P = 140 P = 140 – 100 Profit = $40

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Example…… Mr. Daniel’s family rented a car when they flew to Hawaii for a 3-day vacation. They paid $42 per day and $0.07 for each mile driven. How much did it cost to rent the car for 3 days and drive 200 miles?

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Answer….. Mr. Daniel’s family rented a car when they flew to Hawaii for a 3-day vacation. They paid $42 per day and $0.07 for each mile driven. How much did it cost to rent the car for 3 days and drive 200 miles? Total Cost = (Cost Per Day)(# of Days) + (Cost Per Mile)(# of Miles) Cost = (42)(3) + (200)(0.07) Cost = $126 + $14 Cost = $140

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Answer…… A car repair shop charged Mr. Jacobs $96 for an automotive part plus $72 per hour that a mechanic worked to install the part. The total charge was $388. For about how long did the mechanic work to install the part on Mr. Jacob’s car? Total Cost = Base fee + (Charge Per Hour)(# of hours) $388 = $96 + $72(hours) 388 = H 388 – 96 = 72H 292 = 72H H = 4.06 or 4 Hours

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Example…… A car repair shop charged Mr. Jacobs $96 for an automotive part plus $72 per hour that a mechanic worked to install the part. The total charge was $388. For about how long did the mechanic work to install the part on Mr. Jacob’s car?

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Example…… The length of a rectangle is 5 and the area is 35. Find the perimeter of the rectangle.

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Answer…… The length of a rectangle is 5 and the area is 35. Find the perimeter of the rectangle. 1st: Find the width by using the area formula of a rectangle. A = length x width 35 = 5 x width width = 7

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Remember the width = 7…. The length of a rectangle is 5 and the area is 35. Find the perimeter of the rectangle. 2nd: Plug into the formula to find the perimeter. P = 2l + 2w P = 2(5) + 2(7) P = P = 24

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Example…… The perimeter of a rectangle is 20 and the width is 4. Find the area of the rectangle.

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Answer….. The perimeter of a rectangle is 20 and the width is 4. Find the area of the rectangle. 1st: Find the length using the perimeter formula. P = 2w + 2l 20 = 2(4) + 2l 20 = 8 + 2l 12 = 2l l = 6

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Remember the length = 6….. The perimeter of a rectangle is 20 and the width is 4. Find the area of the rectangle. 2nd: Find the area. A = l x w A = 6 x 4 A = 24

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