More on Solving Equations Section 4

Solve: 7x + x – 2x + 9 = 15 Answer: 7x + x – 2x + 9 = 15 6x + 9 = ___________ 6x = 6 x = 1

Grouping Symbols…… You might have to distribute before you combine like terms.

Solve: 2(x + 3) = x + 7 Answer: 2(x + 3) = x + 7 2x + 6 = x + 7 -x -x ____________ x + 6 = _____________ x = 1

Solve: 2(2x + 3) = 18 Answer: 2(2x + 3) = 18 4x + 6 = ____________ 4x = 12 x = 3

Solve 4(2x) + 5 – 3x = x + 13 Answer: 4(2x) + 5 – 3x = x x + 5 – 3x = x x + 5 = x x -x ________________ 4x + 5 = ________________ 4x = 8 x = 2

Solve: 2(x+5)= 3(x + 2) + x Answer: 2x + 10 = 3(x + 2) + x 2x + 10 = 3x x 2x + 10 = 4x x -4x __________________ -2x + 10 = __________________ -2x = -4 x = 2

Solve: 2(3x + 2) = 2(x+8) Answer: 2(3x + 2) = 2x x + 4 = 2x x -2x ________________ 4x + 4 = _________________ 4x = 12 x = 3

Word Problems Section 5

Words that tell you to add…. Plus Increased By Sum More Than

Words that tell you to subtract… Minus Decreased By Difference Less Than

Multiply and Divide Words….. Multiply – 1. Product 2. times Divide – 1. Quotient 2. Ratio of

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 – m 4 + 2x 12 – n 8 – 3x 2y + 5

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

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

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.

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 P = 500 P = 500 – 190 Profit = $310 (This is the answer)

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

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

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?

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

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?

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

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

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

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

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

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

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