AnswersAlgebra IIRational Inequalities

Rational Inequalities — Quiz Answers

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1
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Which inequality is equivalent to the fraction with numerator x minus 6 and denominator x plus 5 is greater than or equal to the fraction with numerator x plus 7 and denominator x plus 3 ?

A
the fraction with numerator 9 x plus 17 and denominator x squared plus 8 x plus 15 is greater than or equal to 0
B
the fraction with numerator negative 13 and denominator x squared plus 8 x plus 15 is greater than or equal to 0
C
the fraction with numerator 2 x squared plus 9 x plus 17 and denominator x squared plus 8 x plus 15 is greater than or equal to 0
D
the fraction with numerator negative 15 x minus 53 and denominator x squared plus 8 x plus 15 is greater than or equal to 0
2
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Which shows all the critical points for the inequality the fraction with numerator x squared minus 9 x and denominator x minus 5 is less than 0 ?

A
x is equal to 0 , x is equal to 5 , and x is equal to 9
B
x is equal to 5
C
x is equal to 0 and x is equal to 9
D
x is equal to negative 3 , x is equal to 0 , x is equal to 3 , and x is equal to 5
3

Which graph shows the solution set of the inequality the fraction with numerator x squared plus 10 x plus 16 and denominator x minus 3 is greater than 0 ?

A
Image with description A number line from negative 9 to 3. A segment connects an open circle at negative 8 to an open circle at negative 2. An open circle is at 3 with a ray pointing right.
B
Image with description A horizontal number line is labeled with integers from negative 9 to 3, with the variable 'x' indicated at the right end. A segment connects a closed circle at negative 8 to a closed circle at negative 2. An open circle is at 3 with a ray extending to the right.
C
Image with description A number line from negative 9 to 3. A segment connects a closed circle at negative 8 to a closed circle at negative 2. An open circle is at 3 with a ray pointing right.
D
Image with description A horizontal number line is labeled with integers from negative 9 to 3, with the variable 'x' indicated at the right end. An open circle is at negative 8 with a ray pointing left. A segment connects an open circle at 2 to an open circle at 3.
4

Which graph shows the solution set of the fraction with numerator x minus 1 and denominator x minus 3 is less than 0 ?

A
Image with description A number line from negative 5 to 5. A segment connects an open circle at 1 to an open circle at 3.
B
Image with description A number line from negative 5 to 5. A closed circle is at 1 with a ray pointing left. An open circle is at 3 with a ray pointing right.
C
Image with description A number line from negative 5 to 5. A segment connects a closed circle at 1 to an open circle at 3.
D
Image with description A number line from negative 5 to 5. An open circle is at 1 with a ray pointing left. An open circle is at 3 with a ray pointing right.
5

What is the solution of the fraction with numerator x plus 8 and denominator 5 x minus 1 is greater than 0 ?

A
negative 8 is less than x comma x is less than 1 fifth
B
x is less than negative 8 or x is greater than 1 fifth
C
x is less than or equal to negative 8 or x is greater than 1 fifth
D
negative 8 is less than or equal to x comma x is less than 1 fifth
6

The critical points of a rational inequality are negative 1 , 3 , and 4 Which set of points can be tested to find a complete solution to the inequality?

A
x is equal to negative 1 , x is equal to 3 , and x is equal to 4
B
x is equal to negative 3 , x is equal to 1 , x is equal to 3 point 5 , and x is equal to 5
C
x is equal to negative 2 , x is equal to 2 , and x is equal to 5
D
x is equal to 1 and x is equal to 3 point 5
7

Which graph shows the solution set of the fraction with numerator x minus 9 and denominator 7 x plus 2 is less than or equal to 0 ?

A
Image with description A horizontal x-axis number line with tick marks labeled from negative 1 to 10 in increments of 1. Draw the thick red line from an open circle at negative 0 point 3 to the open circle at 9 and extend this line infinitely with arrowhead to the left and right.
B
Image with description A horizontal x-axis number line with tick marks labeled from negative 1 to 10 in increments of 1. Left Interval: Starts with an open circle at approximately "negative 0 point 3" highlighted by a thick red line ending in a leftward-pointing arrowhead. Right Interval: Starts with an open circle at 9, highlighted by a thick red line ending in a rightward-pointing arrowhead.
C
Image with description A horizontal x-axis number line with tick marks labeled from negative 1 to 10 in increments of 1. Starts with an open circle at approximately "negative 0 point 3" highlighted by a thick red line ending in a leftward-pointing arrowhead. Right Interval: Starts with a solid, filled-in red circle at 9, highlighted by a thick red line ending in a rightward-pointing arrowhead.
D
Image with description A horizontal x-axis number line with tick marks labeled from negative 1 to 10 in increments of 1. Draw the thick red line from an open circle at negative 0 point 3 to the closed circle at 9 and extend this line infinitely with arrowhead to the left and right.
8

The critical points of a rational inequality are x is equal to negative 4 and x is equal to 2 Which set of points can be tested to find a complete solution to the inequality?

A
x is equal to negative 4 , x is equal to 0 , and x is equal to 2
B
x is equal to negative 4 and x is equal to 2
C
x is equal to negative 5 and x is equal to 3
D
x is equal to negative 5 , x is equal to 0 , and x is equal to 3
9

Which shows all the critical points for the inequality the fraction with numerator x squared minus 4 and denominator x squared minus 5 x plus 6 is less than 0 ?

A
x is equal to 2 and x is equal to 3
B
x is equal to negative 3 , x is equal to negative 2 , and x is equal to 2
C
x is equal to negative 2 , x is equal to 2 , and x is equal to 3
D
x is equal to negative 2 and x is equal to 2
10

Which shows all the critical points for the inequality the fraction with numerator 2 x plus 5 and denominator x minus 2 is greater than or equal to the fraction with numerator x minus 1 and denominator x minus 2 ?

A
x is equal to negative 6 and x is equal to 2
B
x is equal to 2
C
x is equal to negative 4 and x is equal to 2
D
x is equal to negative 5 halves , x is equal to 1 , and x is equal to 2

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