Understanding and Solving Inequalities

This video introduces solving linear inequalities, emphasizing the key rule of flipping the inequality when multiplying or dividing by a negative number. It provides a step-by-step solution to the inequality 3x - 6 > 8x + 7, explaining each step clearly. The video concludes with an explanation of interval notation and how to graph the solution on a number line.

What is the main rule to remember when solving linear inequalities?

• Flip the inequality sign when multiplying or dividing by a negative number.

• Multiply both sides by zero.

• Always add the same number to both sides.

• Subtract the same number from both sides.

In the inequality 3x - 6 > 8x + 7, what is the first step to solve it?

• Multiply both sides by 8.

• Subtract 3x from both sides.

• Add 6 to both sides.

• Divide both sides by 3.

After subtracting 3x from both sides, what is the resulting inequality?

• 3x - 6 > 5x + 7

• -6 > 5x + 7

• -6 > 8x + 7

• 3x > 8x + 7

What happens to the inequality sign when dividing both sides by a positive number?

• It becomes an equal sign.

• It remains unchanged.

• It flips direction.

• It disappears.

How can the inequality -13/5 > x be rewritten?

• x < -13/5

• x = -13/5

• x > -13/5

• -13/5 < x

What does an open circle on a number line represent?

• The solution is zero.

• The solution is infinite.

• The number is not included in the solution.

• The number is included in the solution.

In interval notation, what symbol is used to indicate that a number is not included?

• Square brackets [ ]

• Angle brackets < >

• Parentheses ( )

• Curly braces { }

What is the interval notation for the solution x < -13/5?

• [-13/5, ∞)

• (-13/5, ∞)

• (-∞, -13/5)

• (-∞, -13/5]

What does the interval notation (-∞, -13/5) represent?

• All numbers greater than -13/5

• All numbers less than -13/5

• All numbers greater than or equal to -13/5

• All numbers equal to -13/5

Why is it important to use parentheses around negative infinity in interval notation?

• Because infinity is always included.

• Because infinity is never included.

• Because it indicates a closed interval.

• Because it represents a finite number.