SOPHIA COLLEGE ALGEBRA
UNIT 2 MILESTONE
,You passed this Milestone
15 questions were answered correctly.
5 questions were answered incorrectly.
1
The relationship between the actual air temperature x (in degrees Fahrenheit) and the temperature y
adjusted for wind chill (in degrees Fahrenheit, given a 20 mph wind) is given by the following formula:
y = -22 + 1.4x
Estimate the actual temperature if the temperature adjusted for wind chill is -15 degrees Fahrenheit.
5 degrees Fahrenheit
-15 degrees Fahrenheit
-5 degrees Fahrenheit
-25 degrees Fahrenheit
RATIONALE
The temperature adjusted for wind chill is given by this equation. The wind chill is -15 degrees, so
substitute this value for y.
Once y is replaced by -15, we can solve for x. First, add 22 to both sides to undo the -22.
On the left side, we will now have 7 because -15 plus 22 equals 7. On the right side, we are left
with 1.4x. To isolate x, divide both sides by 1.4.
7 divided by 1.4 is equal to 5. The actual temperature is 5 degrees.
CONCEPT
Isolating Variables
2
Consider the following subset of the real number line
, How can this set be expressed using inequalities?
-3 > x ≥ 1
-3 < x ≤ 1
-3 ≥ x > 1
-3 ≤ x < 1
RATIONALE
This number line represents a range of values, which indicates that x will be between the two
numbers, -3 and 1. The bracket [ at -3 indicates that we can include the exact value of -3 in our
solution, so use the inequality sign for less than or equal to: ≤. The parentheses ) at 1 indicates
that we cannot include the exact value of 1 in our solution, so use the inequality sign for less
than, <.
This inequality states that x is between and including -3, and 1, but does not include 1.
CONCEPT
Introduction to Inequalities
3
Imagine that 7y + 6 = 36 and y = 2x + 1.
Which of the following equations is equivalent to 7y + 6 = 36, but written only in terms of x?
7x + 7 = 30
14x + 1 = 36
UNIT 2 MILESTONE
,You passed this Milestone
15 questions were answered correctly.
5 questions were answered incorrectly.
1
The relationship between the actual air temperature x (in degrees Fahrenheit) and the temperature y
adjusted for wind chill (in degrees Fahrenheit, given a 20 mph wind) is given by the following formula:
y = -22 + 1.4x
Estimate the actual temperature if the temperature adjusted for wind chill is -15 degrees Fahrenheit.
5 degrees Fahrenheit
-15 degrees Fahrenheit
-5 degrees Fahrenheit
-25 degrees Fahrenheit
RATIONALE
The temperature adjusted for wind chill is given by this equation. The wind chill is -15 degrees, so
substitute this value for y.
Once y is replaced by -15, we can solve for x. First, add 22 to both sides to undo the -22.
On the left side, we will now have 7 because -15 plus 22 equals 7. On the right side, we are left
with 1.4x. To isolate x, divide both sides by 1.4.
7 divided by 1.4 is equal to 5. The actual temperature is 5 degrees.
CONCEPT
Isolating Variables
2
Consider the following subset of the real number line
, How can this set be expressed using inequalities?
-3 > x ≥ 1
-3 < x ≤ 1
-3 ≥ x > 1
-3 ≤ x < 1
RATIONALE
This number line represents a range of values, which indicates that x will be between the two
numbers, -3 and 1. The bracket [ at -3 indicates that we can include the exact value of -3 in our
solution, so use the inequality sign for less than or equal to: ≤. The parentheses ) at 1 indicates
that we cannot include the exact value of 1 in our solution, so use the inequality sign for less
than, <.
This inequality states that x is between and including -3, and 1, but does not include 1.
CONCEPT
Introduction to Inequalities
3
Imagine that 7y + 6 = 36 and y = 2x + 1.
Which of the following equations is equivalent to 7y + 6 = 36, but written only in terms of x?
7x + 7 = 30
14x + 1 = 36
