Rational Inequalities — Quiz

Question 4 • Algebra II

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

Answer

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.

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.

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.

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.

Explanation

The fraction is negative when its numerator and denominator have opposite signs. The critical values are x = 1, where the numerator is zero, and x = 3, where the fraction is undefined; testing a value between them, such as x = 2, gives (2 − 1)/(2 − 3) = −1. Thus the solution is 1 < x < 3, shown by choice A with open circles at both endpoints.

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