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…..

1.
2.
Multiply –
Product
times

1.
2.
Divide –
Quotient
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.

Let’s define the
variables first:

Let C = Cost
Let P = Profit
Let SP = Selling
Price


Find the profit

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:

2nd find the profit:

2C – 60 = 140
2C = 140 + 60
2C = 200
C = $100

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 3day 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=lxw
A=6x4
A = 24