Understanding Compound Inequalities and Solutions

The video tutorial explains how to solve compound inequalities, which are two or more inequalities connected by 'or' or 'and'. It demonstrates solving two inequalities separately and combining their solutions using the union concept. The tutorial includes step-by-step solutions for each inequality, graphing the solutions on a number line, and expressing the final solution using interval notation. The video emphasizes understanding the process of solving inequalities with variables on both sides and the importance of reversing the inequality symbol when dividing by a negative number.

What is a compound inequality?

• An equation with no solution

• A single inequality with a variable

• Two or more inequalities connected by 'or' or 'and'

• An equation with two variables

What does the word 'or' signify in a compound inequality?

• Difference

• Subtraction

• Intersection

• Union

What is the first step in solving the inequality 15x - 3 > 9x + 15?

• Add 3 to both sides

• Multiply by 2

• Subtract 9x from both sides

• Divide by 6

What is the solution to the inequality 15x - 3 > 9x + 15?

• x ≤ 3

• x > 3

• x < 3

• x = 3

What must you remember when dividing by a negative number in an inequality?

• Keep the inequality symbol the same

• Multiply by the reciprocal

• Reverse the inequality symbol

• Add the same number to both sides

What is the solution to the inequality -23 + 4x ≥ 12x + 1?

• x ≤ -3

• x ≥ -3

• x < -3

• x > -3

How is the solution of a compound inequality expressed using interval notation?

• Using a union of intervals

• Using a single interval

• Using a difference of intervals

• Using a product of intervals

What does a square bracket in interval notation indicate?

• The endpoint is not included

• The interval is infinite

• The interval is empty

• The endpoint is included

What is the interval notation for the solution x > 3?

• (3, ∞)

• [3, ∞)

• (3, ∞]

• [3, ∞]

What is the interval notation for the solution x ≤ -3?

• (-∞, -3]

• (-∞, -3)

• (-3, ∞)

• [-3, ∞)