Understanding Linear Inequalities

This video tutorial covers solving linear inequalities in one variable, highlighting the key difference from equations: reversing the inequality symbol when multiplying or dividing by a negative number. It provides examples to illustrate the process, including graphing solutions and using interval notation. The tutorial emphasizes careful handling of inequality symbols during operations.

What is the key difference between solving linear equations and linear inequalities?

• The use of addition and subtraction

• The requirement to graph the solution

• The need to reverse the inequality symbol when multiplying or dividing by a negative number

• The presence of variables

Why must the inequality symbol be reversed when dividing both sides by a negative number?

• To maintain the truth of the inequality

• To simplify the equation

• To eliminate the variable

• To make the inequality false

What happens to the inequality symbol when both sides of an inequality are multiplied by a negative number?

• It is reversed

• It remains the same

• It becomes an equation

• It is removed

In the example where 3x > x + 6, what is the solution for x?

• x = 3

• x ≤ 3

• x > 3

• x < 3

How is the solution set for x > 3 represented in interval notation?

• (3, ∞)

• [3, ∞)

• (3, ∞]

• [3, ∞]

In solving inequalities, what does an open point on a graph indicate?

• The solution is undefined

• The solution is infinite

• The number is not included in the solution

• The number is included in the solution

In the inequality 3 - 5a ≤ 2a + 10, what is the solution for a?

• a < -1

• a ≥ -1

• a ≤ -1

• a > -1

What type of bracket is used in interval notation to indicate that a number is included in the interval?

• Curly bracket

• Square bracket

• Angle bracket

• Rounded parenthesis

In the inequality -5x - 10 ≥ -3x - 12, what is the solution for x?

• x > 1

• x < 1

• x ≥ 1

• x ≤ 1

How is the solution set for x ≤ 1 represented in interval notation?

• (-∞, 1]

• (-∞, 1)

• [1, ∞)

• (1, ∞)