More on Solving Equations

Section 4

Solve:

7x + x – 2x + 9 = 15 Answer: 7x + x – 2x + 9 = 15

6x + 9 = 15

-9 -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 = 7 -6 -6 _____________ x = 1

Solve:

2(2x + 3) = 18 Answer:

2(2x + 3) = 18

4x + 6 = 18

-6 -6

____________

4x = 12

x = 3

Solve

4(2x) + 5 – 3x = x + 13 Answer: 4(2x) + 5 – 3x = x + 13

8x + 5 – 3x = x + 13

5x + 5 = x + 13

-x -x

________________

4x + 5 = 13

-5 -5

________________

4x = 8

x = 2

Solve:

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

2x + 10 = 3x + 6 + x

2x + 10 = 4x + 6

-4x -4x

__________________

-2x + 10 = 6

-10 -10

__________________

-2x = -4

x = 2

Solve:

2(3x + 2) = 2(x+8) Answer: 2(3x + 2) = 2x + 16

6x + 4 = 2x + 16

-2x -2x

________________

4x + 4 = 16

-4 -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 5

9 + 2 5 – m 4 + 2x 12 – 7 7 + 5n

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. 190 + 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.

1st find the cost:

2C – 60 = 140

2C = 140 + 60

2C = 200

C = $100

2nd find the profit:

C + P = SP

100 + 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 = 96 + 72H 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.

1st: 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.

2nd: Plug into the formula to find the perimeter.

P = 2l + 2w

P = 2(5) + 2(7)

P = 10 + 14

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.

1st: 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