Station 1
The rectangle below has an area of at least 30 units. Write the inequality, solve for x,
and graph the inequality.
4x - 2
5
Station 1 key
𝟓(𝟒𝒙 − 𝟐) ≥ 𝟑𝟎
𝟐𝟎𝒙 − 𝟏𝟎 ≥ 𝟑𝟎
𝟐𝟎𝒙 ≥ 𝟒𝟎
𝒙≥𝟐
–5 –4 –3 –2 –1
0
1
2
3
4
5
Station 2
Which of the following is NOT in the solution set to the inequality below?
𝟒
𝒙 − 𝟐 < −𝟑
𝟓
A) -2
B)
−𝟑
𝟐
C)
−𝟏
𝟐
D)
−𝟐𝟎
𝟑
Station 2 key
𝟒
𝒙 − 𝟐 < −𝟑
𝟓
𝟒
𝒙 < −𝟏
𝟓
𝟒𝒙 < −𝟓
−𝟓
𝒙<
𝟒
Since the solution set includes all values of x that are less than
that
is
NOT
in
the
solution
set
because
−𝟏
𝟐
is
−𝟓
𝟒
, C is the only answer
NOT
less
than
−𝟓
𝟒
.
Station 3
Which inequalities have NO SOLUTION or ALL REAL NUMBERS as their answer?
(try them all)
A) 𝟒(𝒙 − 𝟑) + 𝟐𝒙 > 𝟔𝒙 + 𝟏
D) 𝟏𝟎𝒙 − 𝟕 > 𝟓(𝟐𝒙 + 𝟒)
B) – 𝒙 + 𝟒(𝒙 + 𝟐) < 𝟒𝒙 − 𝟐
E) 𝟔𝒙 + 𝟏 > 𝟐(𝟑𝒙 − 𝟒) − 𝟓
C) 𝟓(𝒙 + 𝟏) − 𝟔 < 𝟑𝒙 + 𝟐(𝒙 + 𝟒)
Station 3 key
ANSWER: A and D are no solution; C and E are all real numbers
A) 4(𝑥 − 3) + 2𝑥 > 6𝑥 + 1
−12 > 1
-12 is not greater than 1 so this is false
B) – 𝑥 + 4(𝑥 + 2) < 4𝑥 − 2
– 𝑥 + 4𝑥 + 8 < 4𝑥 − 2
3𝑥 + 8 < 4𝑥 − 2 this will have a solution
C) 5(𝑥 + 1) − 6 < 3𝑥 + 2(𝑥 + 4)
5𝑥 + 5 − 6 < 3𝑥 + 2𝑥 + 8
−1 < 8 this is a true statement because -6 is less than 8
D) 10𝑥 − 7 > 5(2𝑥 + 4)
−7 > 20
this is a false statement because -7 is not greater than 20
E) 6𝑥 + 1 > 2(3𝑥 − 4) − 5
6𝑥 + 1 > 6𝑥 − 8 − 5
1 > −13
this is a true statement because 1 is greater than -13
Station 4
Write, solve, and graph the following compound inequality:
Twice the quantity of the sum of a number and four is at most
fourteen OR three times a number is at least twelve.
Station 4 key
Twice the quantity of the sum of a number and four is at most fourteen.
2(𝑛 + 4) ≤ 14
2𝑛 + 8 ≤ 14
2𝑛 ≤ 6
𝑛≤3
OR three times a number is at least twelve
3𝑛 ≥ 12
𝑛≥4
𝑛 ≤ 3 𝑜𝑟 𝑛 ≥ 4
–5 –4 –3 –2 –1
0
1
2
3
4
5
Station 5
Describe the error(s) in the following problem, then solve and graph correctly:
𝟒 < −𝟐𝒙 + 𝟑 < 𝟗
𝟒 < −𝟐𝒙 < 𝟔
−𝟐 > 𝒙 > −𝟑
−𝟑 < 𝒙 < −𝟐
–5 –4 –3 –2 –1
0
1
2
3
4
5
Station 5 key
1) 3 was subtracted from the 9 but not the 4
2) Closed circles were used instead of open circles
𝟒 < −𝟐𝒙 + 𝟑 < 𝟗
𝟏 < −𝟐𝒙 < 𝟔
−𝟏
> 𝒙 > −𝟑
𝟐
−𝟑 < 𝒙 < −
–5 –4 –3 –2 –1
0
1
𝟏
𝟐
2
3
4
5
Station 6
Rewrite the equations so that y is a function of x:
1. 𝟐𝒙 + 𝟑𝒚 = −𝟔
𝟐
2. 𝟑 𝒙 − 𝟐𝒚 = 𝟒
𝟏
3. −𝒙 + 𝟓 𝒚 = −𝟕
4. −𝟖𝒙 − 𝟐𝒚 = 𝟎
Station 6 key
1. 𝟐𝒙 + 𝟑𝒚 = −𝟔
𝟑𝒚 = −𝟐𝒙 − 𝟔
𝟐
𝒚=− 𝒙−𝟐
𝟑
2.
𝟐
𝟑
𝒙 − 𝟐𝒚 = 𝟒
𝟐
−𝟐𝒚 = − 𝒙 + 𝟒
𝟑
𝟏
𝒚= 𝒙−𝟐
𝟑
𝟏
3. −𝒙 + 𝟓 𝒚 = −𝟕
𝟏
𝒚=𝒙−𝟕
𝟓
𝒚 = 𝟓𝒙 − 𝟑𝟓
4. −𝟖𝒙 − 𝟐𝒚 = 𝟎
−𝟐𝒚 = 𝟖𝒙
𝒚 = −𝟒𝒙
Station 7
Solve the equations for the given variables.
𝑨𝒍 + 𝒈𝒆 = 𝒃𝒓 − 𝒂, 𝒔𝒐𝒍𝒗𝒆 𝒇𝒐𝒓 𝒈
𝑮𝑯 = 𝑶𝑺 − 𝑻, 𝒔𝒐𝒍𝒗𝒆 𝒇𝒐𝒓 𝑶
𝟓𝒑 − 𝟑𝒓 = 𝒅, 𝒔𝒐𝒍𝒗𝒆 𝒇𝒐𝒓 𝒓
𝒕(𝟏 − 𝒔) − 𝒉 = 𝒅𝒃, 𝒔𝒐𝒍𝒗𝒆 𝒇𝒐𝒓 𝒔
Station 7 key
𝑨𝒍 + 𝒈𝒆 = 𝒃𝒓 − 𝒂 , 𝒔𝒐𝒍𝒗𝒆 𝒇𝒐𝒓 𝒈
𝟓𝒑 − 𝟑𝒓 = 𝒅 , 𝒔𝒐𝒍𝒗𝒆 𝒇𝒐𝒓 𝒓
𝒈𝒆 = −𝑨𝒍 + 𝒃𝒓 − 𝒂
−𝟑𝒓 = 𝒅 − 𝟓𝒑
𝒈=
−𝑨𝒍 + 𝒃𝒓 − 𝒂
𝒆
𝒓=
𝒅 − 𝟓𝒑
−𝟑
𝒕(𝟏 − 𝒔) − 𝒉 = 𝒅𝒃 , 𝒔𝒐𝒍𝒗𝒆 𝒇𝒐𝒓 𝒔
𝑮𝑯 = 𝑶𝑺 − 𝑻 , 𝒔𝒐𝒍𝒗𝒆 𝒇𝒐𝒓 𝑶
𝑮𝑯 + 𝑻 = 𝑶𝑺
𝑮𝑯 + 𝑻
=𝑶
𝑺
𝒕(𝟏 − 𝒔) = 𝒅𝒃 + 𝒉
𝟏−𝒔=
𝒅𝒃 + 𝒉
𝒕
𝒅𝒃 + 𝒉
−𝒔 =
−𝟏
𝒕
𝒔=−
𝒅𝒃 + 𝒉
+𝟏
𝒕
Station 8
1. What is the slope of the line through
(1,3) and (4,-1)
2. A line has a slope of
−𝟓
𝟑
. Though which
two points could this line pass?
a) (12,13) (17,10) b) (0,7) (3,10)
c) (16,15) (13,10) d) (11, 13) (8,18)
3. A train traveling at a constant rate is
120 km from its destination at 1:00 pm.
The train is 88 km from its destination at
1:24 pm. Determine the rate of change.
Station 8 Key
1.
−𝟒
𝟑
2. (11, 13) (8,18)
𝟒
3. 𝟑 km per minute