AnswersAZ-Common Core Algebra II ARational Inequalities

Rational Inequalities Answers

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1
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Describe the steps you would use to solve the following inequality:

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Answer:

Subtract 2 from both sides and combine over a common denominator to obtain (7 − 3x)/(2x − 3) > 0. Identify the critical values x = 3/2 and x = 7/3, then test the intervals they create. The expression is positive on (3/2, 7/3), so the solution is (3/2, 7/3); exclude the endpoints because the inequality is strict and the denominator is zero at x = 3/2.

2
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Solve:

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A
–4 < x < –2
B
–2 < x < 4
C
–2 < x < –4
D
–4 < x < 2
3

Does your answer include the following?

A
Rewrite the inequality so there is a single rational expression on one side, and 0 on the other.
B
Combine under a common denominator.
C
Test points in the critical regions.
D
Construct the solution.
4

Solve:

Question illustration
A
x < 4
B
x > –4
C
x > 4
D
x < –4
5

Solve the inequality and write the solution in interval notation:

Question illustration
A
(-5, 6)
B
[-5, 6)
C
Option
D
Option
6

Which interval(s) contains viable travel rates for the boat on the first leg of the trip?

A
(0,4] only
B
(0,4] and (10,30]
C
[4,10) and (10,30]
D
(10,30] only
7

Solve the inequality and write the solution in interval notation:

Question illustration
A
Option
B
Option
C
Option
D
Option
8

Solve the inequality. Which intervals are included in the solution? Check all that apply.

A
Option
B
(0, 4]
C
[4, 10)
D
(10, 30]
E
Option

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