More on Solving Equations Grouping Symbols on Both

More on Solving Equations

Grouping Symbols on Both Sides…… n You might have to distribute before you combine like terms.

Solve: 2(x+5)= 3(x + 2) + x n Answer: 2 x + 10 = 3(x + 2) + x 2 x + 10 = 3 x + 6 + x 2 x + 10 = 4 x + 6 -4 x _________ -2 x + 10 = 6 -10 _________ -2 x = -4 x=2

Solve: 2(3 x + 2) = 2(x+8) n Answer: 2(3 x + 2) = 2 x + 16 6 x + 4 = 2 x + 16 -2 x ________ 4 x + 4 = 16 -4 -4 _________ 4 x = 12 x=3

Word Problems

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

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

Multiply and Divide Words…. .

Write the mathematical statement for the following…. . n n n n 9 increased by 2 5 decreased by m Sum of 4 and 2 x 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 n 9+2 5–m 4 + 2 x 12 – 7 7 + 5 n n 8 – 3 x n 2 y + 5 n n

You Try…. . n The sum of 7 and 3 times a number n 4 times Harry’s age increased by 2 n 8 pounds less than twice wanda’s weight n 7 + 3 n n 4 h + 2 n 2 w - 8

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

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

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

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

Example…… n 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…. . n 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? n Total Cost = (Cost Per Day)(# of Days) + (Cost Per Mile)(# of Miles) n Cost = (42)(3) + (200)(0. 07) Cost = $126 + $14 Cost = $140 n n

Answer…… n 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? n Total Cost = Base fee + (Charge Per Hour)(# of hours) n $388 = $96 + $72(hours) n 388 = 96 + 72 H 388 – 96 = 72 H 292 = 72 H H = 4. 06 or 4 Hours

Example…… n 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?

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

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

Remember the width = 7…. n The length of a rectangle is 5 and the area is 35. Find the perimeter of the rectangle. n n 2 nd: Plug into the formula to find the perimeter. P = 2 l + 2 w P = 2(5) + 2(7) P = 10 + 14 P = 24

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

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

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