Understanding Linear Inequalities

This video tutorial covers solving linear inequalities in one variable. It explains the difference between linear equations and inequalities, highlighting that inequalities have multiple solutions. The tutorial demonstrates how to express solutions using inequalities, graphs, and interval notation. It provides examples of solving inequalities, emphasizing the need to reverse the inequality symbol when multiplying or dividing by a negative number. The video also shows how to use graphing calculators to find solutions graphically.

What is the main difference between linear equations and linear inequalities?

• Linear inequalities have more solutions than linear equations.

• Linear equations have equal signs, while linear inequalities have inequality signs.

• Linear inequalities have equal signs.

• Linear equations have inequality signs.

How can solutions to linear inequalities be expressed?

• Only using graphs.

• Using equations and graphs.

• Using inequalities, graphs, or interval notation.

• Only using interval notation.

In the inequality x < 2, why is the circle open on the graph?

• Because 2 is included in the solution.

• Because 2 is not included in the solution.

• Because the inequality is greater than.

• Because the inequality is less than or equal to.

What does a closed point on a graph indicate in terms of inequality solutions?

• The inequality is not strict.

• The number is not included in the solution.

• The number is included in the solution.

• The inequality is strict.

What is the graphical representation of the inequality x > 2?

• A closed circle on 2 with an arrow to the right.

• An open circle on 2 with an arrow to the right.

• An open circle on 2 with an arrow to the left.

• A closed circle on 2 with an arrow to the left.

What happens to the inequality symbol when you multiply or divide both sides by a negative number?

• It remains the same.

• It disappears.

• It becomes an equal sign.

• It reverses direction.

When solving the inequality -3x > -28, what is the correct solution after dividing by -3?

• x > -28/3

• x < -28/3

• x > 28/3

• x < 28/3

What is the interval notation for the inequality x ≥ -3?

• (-3, ∞)

• [-3, ∞)

• (-∞, -3]

• [-3, ∞]

How do you graphically determine the solution to an inequality using a graphing calculator?

• By finding where one line is below or equal to the other.

• By checking where one line is above the other.

• By checking where the lines are parallel.

• By finding where the lines intersect.

What is the purpose of using a graphing calculator in solving inequalities?

• To check solutions graphically.

• To graph the solution set.

• To find the exact numerical solution.

• To avoid algebraic manipulation.