Solving Nonlinear Inequalities

The video tutorial explains how to solve nonlinear inequalities by using a number line to identify positive and negative intervals. It covers two examples: one involving a product of factors and another involving a rational expression. The tutorial emphasizes finding zeros and determining the sign of intervals to solve inequalities.

What is the main focus when solving nonlinear inequalities?

• Solving for y

• Calculating the derivative

• Identifying where the expression is positive or negative

• Finding the exact value of x

What is the first step in solving the inequality x + 3 times x - 9?

• Graphing the equation

• Finding the zeros of the factors

• Calculating the derivative

• Solving for y

Where is the zero of the factor x + 3 located on the number line?

• At x = 3

• At x = -3

• At x = 9

• At x = -9

What is the sign of x + 3 to the right of its zero?

• Undefined

• Negative

• Positive

• Zero

What is the sign of x - 9 to the left of its zero?

• Undefined

• Zero

• Negative

• Positive

What is the solution interval for x + 3 times x - 9 being greater than or equal to 0?

• (-∞, 9)

• (-3, 9)

• (-∞, 3) ∪ (9, ∞)

• (-∞, -3) ∪ (9, ∞)

What is the new inequality introduced in the video?

• x times (x + 2) divided by (x - 5) is greater than or equal to 0

• x times (x + 2) divided by (x - 5) is equal to 0

• x times (x + 2) divided by (x - 5) is less than or equal to 0

• x times (x + 2) divided by (x - 5) is greater than 0

Where is the zero of the factor x located on the number line?

• At x = 0

• At x = -2

• At x = -5

• At x = 5

What is the sign of x + 2 to the right of its zero?

• Negative

• Positive

• Zero

• Undefined

What is the sign of x - 5 to the left of its zero?

• Undefined

• Zero

• Positive

• Negative