Understanding Compound Inequalities

The video tutorial explains how to solve compound inequalities, which consist of two inequalities connected by 'or'. It demonstrates solving each inequality separately, graphing the solutions on a number line, and combining them using union. The tutorial also covers expressing the solution in interval notation, emphasizing the use of open parentheses for non-inclusive values and the concept of infinity.

What does a compound inequality consist of?

• Two inequalities connected by 'and'

• A single inequality

• Two inequalities connected by 'or'

• Two equations connected by 'and'

What is the first step in solving the inequality 2X - 10 < -14?

• Multiply both sides by 2

• Divide both sides by 2

• Add 10 to both sides

• Subtract 10 from both sides

When dividing both sides of an inequality by a positive number, what happens to the inequality symbol?

• It reverses

• It is removed

• It stays the same

• It becomes an equal sign

What is the solution to the inequality 2X - 10 < -14?

• X < -2

• X > -2

• X ≥ -2

• X = -2

What must you remember when dividing both sides of an inequality by a negative number?

• The inequality symbol stays the same

• The inequality symbol reverses

• The inequality symbol is removed

• The inequality becomes an equation

What is the solution to the inequality -3X + 2 < -10?

• X ≤ 4

• X > 4

• X = 4

• X < 4

What does the 'or' in a compound inequality indicate?

• Union of solutions

• Intersection of solutions

• Difference of solutions

• Product of solutions

How is the solution to a compound inequality expressed in interval notation?

• Using square brackets for all numbers

• Using rounded parentheses for open intervals

• Using curly braces for all numbers

• Using square brackets for open intervals

What does the 'U' symbol represent in interval notation?

• Product

• Intersection

• Difference

• Union

What is the interval notation for the solution X < -2 or X > 4?

• (-∞, -2] U [4, ∞)

• [-∞, -2] U [4, ∞]

• [-∞, -2) U (4, ∞]

• (-∞, -2) U (4, ∞)