Algebra 2
Name:
Date:
Review 3: Equations and Changing Units
Directions: Do all work on a separate sheet of paper. Show all work. Check your
answer after each problem. Only use your calculator on section V.
I. Solving equations. Solve the following equations for x. Hint: when fractions are
involved you can multiple both sides by the LCD.
3
2
Example: x  1  (3x  1)
5
3
LCD =
1. 2x  1  9
2. 2  3(4  x)  3
3. 3(2 x  5)  (2  3x)  5  2(3x  4)
4.
3
x  5  3
4
6.
5 4
 x 9
7 7
8.
4
x2
(2 x  4)  3 
3
3
5.
7.
9.
2
x  4  x 1
3
5
1
x 1 
x2
3
2
1
2
1
( x  2)  (2 x  1) 
4
3
6


10.
2 1
1
1
 x   1  x 
5 3
4
10
II. Solving equations for variables:
1. Solve for y in terms of x: 2 x  6 y  x  3
2. Solve for b in terms of the other variables: 2b  3(a  2b)  6a  11
3. Solve for c in terms of the other variables: d (2c  x)  3
4. The surface area of a cylinder is S  2r 2  2rh . Solve this for h.
III. Simplifying Expressions
2
5
x
is an expression and not an equation because there is no equals sign. Can we
3
2
multiply by the LCD of 6 and simplify it to 4 x  15 ? Briefly explain why or why not.
IV. Analyzing Units
Perform the following calculations. Be sure to specify the units of your answer. Units can
be cancelled.
70 miles
60 dollars 1 month

1. 3 hours 
2.
1 hour
1 month 30 days
3. 36 eggs 
1 dozen eggs
12 eggs
V. Changing Units
One approach to changing units is to multiply an expression by a fraction that is
mathematically equivalent to 1 (so it does not change the value), but does involve a
change in units. Use a calculator on this section and give your answers as decimals.
1. How many meters are there in a mile? (Note: 2.54 cm =1 in and 5280 ft = 1 mile ).
2. Jerry has a cell phone plan in which he pays $40 every month.
a. What are the units for the amount per month that he pays?

b. How much does Jerry pay per day? Use correct units in your answer. (You may
assume a 31 day month).
3. A recent survey shows the typical price of a Big Mac in the US to be about $2.75.
a. In Kuwait, the price is 2.14 dinars. Each Kuwaiti dinar is currently worth $3.42.
What is the price of a Big Mac in Kuwait in US dollars?
b. Not far from Kuwait, in the United Arab Emirates (UAE), a Big Mac sells for 2.46
dirhams. Each US dollar is worth 3.67 dirhams. What is the dollar price of a Big Mac in
the UAE?
13
14
8
3. x 
4. x  5. x  15 6. x  17 7.
3
3
3
6
5
16
15
x3
x
8. x  9. x  
10. x 
. Section II: 1. y 
(You could also write
13
7
13
13
6
x 1
y   . The next few problems also have answers that could similarly be expressed
6 2
9a  11
xd  3
S  2 r 2
in two ways that are both correct.) 2. b 
3. c 
4. h 
.
8
2d
2 r
Section III: 1. No. We'll discuss why during class. Section IV: 1. 210 miles 2. $2/day (in
dollars
other words, $2 per day) 3. 3 dozen eggs. Section V: 1. 1609.34 meters 2a.
(or
month
dollars per month) 2b. $1.29 / day (or $1.29 per day) 3. $7.32 4. $0.67.
Answers Section I: 1. x  4 2. x 