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
