Name: _______________________
Date: __________________
AU1: Expressions, Equations & Single Variable Inequalities Review
Total: 60 points
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1.
2.
Which number is in the solution set of the inequality 4x  4  36 ?
(a) 9
(c) 7
(b) 8
(d) 6
2
1
3 b  b7
9
3
(a) 30
3.
(b) 18
(c) 90
This portion of a flow chart demonstrates which property?
4  x  5a  2xy   4  x  5a  2xy 
(a) Distributive Property
(b) Commutative Property of Addition
(c) Associative Property of Addition
(d) Associative Property of Multiplication
1
(d) 9
(2pts each)
4.
In order to be admitted for a certain ride at an amusement park, a child must be greater
than 36 inches tall and less than or equal to 48 inches tall. Which graph represents these
conditions?
5.
Ernest works in the shipping department loading shipping crates with boxes. Each empty
crate weighs 150 lbs. How many boxes, each weighing 35 lbs, can Ernest put in the crate
if the total weight is to be at most 850 lbs?
(a) 22
(c) 20
(b) 21
(d) 23
2
Short Answer
Solve the following equations for x. Justify or Check your solution when asked.
If appropriate write identity or no solution. Show all work
(2 points each part)
6.
4x  5  4x  7
8.
 3x  2  9x  6
Justify:
9.
2
9 x  27   36
3
Check:
10.
12x  3  42x  9  4x
7.
11.
3
ax b
a  3x  5x  b
Solve the following inequalities for x and graph the solution on a number line.
Show all work.
(4 pts each)
12.
12x – 3x + 11 > 4x – (17 – 9x)
13.
2x  4  8 or 9x  1  10
14.
1 
15.
x  4 and  x  1  5
2
x33
3
4
16.
Tara owns a pizza shop. The item purchased most frequently from her shop is a large
pizza. For any order, Tara charges $7.00 for each pizza plus $3.00 for delivery services.
Tara made a delivery of pizzas to a party for which she charged $45.00. How many
pizzas did she deliver?
Only an algebraic solution will be accepted.
(4 pts)
17.
The Zonda Information and Telephone Company (ZI&T) calculates a customer’s total
monthly cell phone charge using the formula,
C  b  rm1  t 
Where C is the total cell phone charge, b is a basic monthly fee, r is the rate per minute,
m is the number of minutes used that month, and t is the tax rate.
Solve for m, the number of minutes the customer used that month.
(2 pts)
18.
What value of x makes the perimeters of the figures below equal?
Only an algebraic solution will be accepted.
5
(4 pts)
19.
Suppose it costs $5 to enter a carnival. Each ride costs $1.25. You have $15 to spend at
the carnival.
Write and solve an inequality to determine the greatest number of rides that you can go
on.
(2 pts)
20.
If a  0 and c  b , circle the expression that is greater:
ab  c or ac  b
21.
Use the properties of inequalities to explain your choice.
(4 pts)
Write a mathematical proof of the algebraic equivalence of:
(2 pts)
pq  r  and pr  pq .
6