Inequalities and Interval Notation Concepts

The video tutorial explains how to solve an inequality by factoring and performing sign analysis. It begins with factoring the expression into two binomials and setting each factor to zero to find critical points. These points are plotted on a number line, and intervals are tested to determine the sign of the product in each interval. The solution is expressed in interval notation, indicating where the inequality is greater than zero.

What is the first step in solving the inequality?

• Using the quadratic formula

• Graphing the equation

• Factoring the expression

• Solving for x

What do you do after factoring the expression?

• Divide the factors

• Multiply the factors

• Add the factors together

• Set each factor to zero

What are the critical points obtained from the factors?

• -4 and 3

• 1 and -1

• -3 and 4

• 0 and 5

Why are the intervals open at the critical points?

• Because the inequality is greater than zero

• Because the inequality is less than zero

• Because the inequality is equal to zero

• Because the inequality is undefined

Which test point is suitable for the interval less than -3?

• -2

• -1

• 0

• -4

What is the sign of the product in the interval from -3 to 4?

• Undefined

• Zero

• Negative

• Positive

What is the result of multiplying two negative numbers?

• Negative

• Positive

• Zero

• Undefined

What is the result of multiplying a negative and a positive number?

• Negative

• Positive

• Zero

• Undefined

What is the sign of the product in the interval greater than 4?

• Positive

• Undefined

• Zero

• Negative

In which intervals is the inequality positive?

• (-∞, -3) and (4, ∞)

• (-3, 4)

• (4, ∞)

• (-∞, 4)