Rational Inequalities and Their Solutions

The video tutorial explains how to solve a rational inequality by finding the zeros of the numerator and denominator, plotting them on a number line, and testing intervals with selected values. The solution is expressed using interval notation, highlighting the importance of open and closed points based on the inequality symbol.

What is the first step in solving a rational inequality?

• Determine the zeros of the numerator and denominator.

• Test the intervals with selected values.

• Ensure the inequality is in the correct form.

• Plot the zeros on a number line.

How do you find the zero of the numerator in the inequality r(x) > 0?

• Set the entire inequality to zero.

• Set the denominator to zero.

• Set x - 6 equal to zero and solve for x.

• Set x - 4 equal to zero and solve for x.

What type of points are used for the zeros of the numerator when the inequality symbol is 'greater than'?

• Open points

• Closed points

• Dashed points

• Solid points

What does an open point on the number line indicate?

• The value is a midpoint.

• The value is a boundary point.

• The value is not a possible solution.

• The value is included in the solution.

Which test value satisfies the inequality r(x) > 0 when x = 3?

• The test value is inconclusive.

• The test value is irrelevant.

• The test value does not satisfy the inequality.

• The test value satisfies the inequality.

What is the result when testing the interval with x = 5?

• The interval is undefined.

• The interval is partially true.

• The interval is false.

• The interval is true.

Which test value satisfies the inequality r(x) > 0 when x = 7?

• The test value is irrelevant.

• The test value satisfies the inequality.

• The test value does not satisfy the inequality.

• The test value is inconclusive.

What is the solution of the inequality r(x) > 0 in interval notation?

• (-∞, 6) ∪ (4, ∞)

• (4, 6)

• [4, 6]

• (-∞, 4) ∪ (6, ∞)

What is the graph of the solution for the inequality r(x) > 0?

• x > 4 and x < 6

• x < 4 or x > 6

• x = 4 or x = 6

• x ≤ 4 and x ≥ 6

What notation is used to express the solution of the inequality?

• Graphical notation

• Algebraic notation

• Set notation

• Interval notation