Solving Rational Inequalities in One Variable

What is a rational inequality?

• A function that is always positive

• An inequality with only integers

• An inequality involving rational functions

• An equation with rational numbers

In solving the inequality x - 2 over x + 5 > 2, what is the first step?

• Divide by x

• Multiply both sides by 2

• Transpose 2 to the left-hand side

• Add 5 to both sides

What are critical points in the context of rational inequalities?

• Points where the function is undefined

• Points where the function is maximum

• Points where the numerator and denominator are zero

• Points where the function is minimum

For the inequality x + 3 over x - 2 ≤ 2, which point is included in the solution set?

• x = 7

• x = -2

• x = 3

• x = 2

What is the solution set for the inequality x + 3 over x - 2 ≤ 2?

• (2, 7)

• (2, ∞)

• (-∞, 7]

• (-∞, 2) ∪ (7, ∞)

What is the first step in the generalized method for solving rational inequalities?

• Simplify the inequality

• Transpose all terms to the left-hand side

• Make coefficients positive

• Plot the critical points

How do you determine the sign of the rational function in different regions?

• By checking the sign of the numerator only

• By checking the sign of the denominator only

• By checking the signs of both numerator and denominator

• By checking the sign of the constant term