8/20/2020 Sophia :: Welcome
Score 19/20
You passed this Milestone
19 questions were answered correctly.
UNIT 2 — MILESTONE 2
1 question was answered incorrectly.
1
Find the solution for if .
and
and
and
and
RATIONALE
To solve this equation, we will need to create two separate equations without absolute
value bars.
One equation will contain the expression exactly as it appears within the absolute value
bars. The second equation must consider the case when the expression has the opposite
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value. Next, solve each equation separately, starting with .
To solve for , start by adding to both sides.
On the left, we have only . On the right plus is . Then divide both sides by
to isolate .
The solution for the first equation is . The same process can be applied to the
second equation .
To solve, start by adding to both sides.
On the left, we have only . On the right plus is . Then divide both sides
by to isolate .
The solution for second equation is .
The two solutions to are and .
CONCEPT
Absolute Value Equations
2
Use the FOIL method to evaluate the expression:
RATIONALE
FOIL stands for First, Outside, Inside, Last, and helps us remember how to multiply two
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binomials. Begin by multiplying the first two terms, and .
times equals . Next, multiply the two outside terms, and .
times equals because when you multiply two terms with the same number
under the radical symbol, the result is just that number. Next, multiply the two inside
terms, and .
times equals . Next, multiply the last two terms, and .
equals . Now we can combine all four parts.
After using FOIL, is equal to . Next, identify any
like terms and combine.
We can combine the two constant terms, and , to get . We can also combine the two
radical terms, and , to get . The expression is equal
to .
CONCEPT
Multiplying Radical Expressions
3
Rationalize the denominator and simplify the following expression:
https://www.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/5268644 3/17
Score 19/20
You passed this Milestone
19 questions were answered correctly.
UNIT 2 — MILESTONE 2
1 question was answered incorrectly.
1
Find the solution for if .
and
and
and
and
RATIONALE
To solve this equation, we will need to create two separate equations without absolute
value bars.
One equation will contain the expression exactly as it appears within the absolute value
bars. The second equation must consider the case when the expression has the opposite
https://www.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/5268644 1/17
,8/20/2020 Sophia :: Welcome
value. Next, solve each equation separately, starting with .
To solve for , start by adding to both sides.
On the left, we have only . On the right plus is . Then divide both sides by
to isolate .
The solution for the first equation is . The same process can be applied to the
second equation .
To solve, start by adding to both sides.
On the left, we have only . On the right plus is . Then divide both sides
by to isolate .
The solution for second equation is .
The two solutions to are and .
CONCEPT
Absolute Value Equations
2
Use the FOIL method to evaluate the expression:
RATIONALE
FOIL stands for First, Outside, Inside, Last, and helps us remember how to multiply two
https://www.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/5268644 2/17
, 8/20/2020 Sophia :: Welcome
binomials. Begin by multiplying the first two terms, and .
times equals . Next, multiply the two outside terms, and .
times equals because when you multiply two terms with the same number
under the radical symbol, the result is just that number. Next, multiply the two inside
terms, and .
times equals . Next, multiply the last two terms, and .
equals . Now we can combine all four parts.
After using FOIL, is equal to . Next, identify any
like terms and combine.
We can combine the two constant terms, and , to get . We can also combine the two
radical terms, and , to get . The expression is equal
to .
CONCEPT
Multiplying Radical Expressions
3
Rationalize the denominator and simplify the following expression:
https://www.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/5268644 3/17
