Compound Inequalities and Their Solutions

The video tutorial explains how to solve compound inequalities and express the solution using interval notation. It begins by introducing the concept of compound inequalities, which involve two inequality symbols. The tutorial then focuses on understanding the middle expression and solving two separate inequalities, referred to as the red and blue inequalities. Each inequality is solved step-by-step, with solutions graphed on a number line. The video concludes by interpreting the solution, combining inequalities, and expressing the final answer using interval notation.

What is a compound inequality?

• A single inequality with one condition

• An equation with two variables

• An inequality with two inequality symbols

• An equation with no solutions

What is the first step in solving a compound inequality?

• Finding the intersection of solutions

• Graphing the solution

• Breaking it into two separate inequalities

• Combining the inequalities

How do you solve the inequality 2X + 10 < X + 9?

• Divide both sides by 2

• Add X to both sides

• Subtract X from both sides

• Multiply both sides by 2

What does an open point on a number line indicate?

• The number is the only solution

• The number is not included in the solution

• The number is included in the solution

• The number is a boundary point

What is the result of solving the inequality X + 9 ≤ 3X + 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

• Reverse the inequality symbol

• Subtract the same number from both sides

• Add the same number to both sides

What does a closed point on a number line indicate?

• The number is the only solution

• The number is a boundary point

• The number is not included in the solution

• The number is included in the solution

What is the interval notation for the solution of the compound inequality?

• [-3, -1]

• [-3, -1)

• (-3, -1]

• (-3, -1)

How can the solution of the compound inequality be expressed?

• Using neither a graph nor interval notation

• Using both a graph and interval notation

• Using interval notation only

• Using a graph only

How can the two inequalities be combined into a single expression?

• By multiplying them together

• By subtracting one from the other

• By adding them together

• By placing the variable in the middle