Solving and Graphing Inequalities

The video tutorial explains how to solve an inequality and graph the solution on a number line. It begins with isolating the variable X and treating the inequality like an equation, with a key exception when dividing by a negative number, which requires flipping the inequality sign. The solution is then graphed, showing numbers greater than the solution on a number line, with an open circle indicating that the solution itself is not included.

What is the main goal when solving the given inequality?

• To isolate X

• To find the value of Y

• To graph the solution

• To simplify the equation

What should you do first according to the order of operations?

• Distribute the negative number

• Combine like terms

• Solve for X

• Start with what's inside the parentheses

What is the result of distributing -2 in the expression -2(x - 3)?

• -2x + 6

• -2x - 6

• 2x - 6

• 2x + 6

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

• Add the same number to both sides

• Subtract the same number from both sides

• Flip the inequality sign

• Multiply both sides by a positive number

What is the final inequality after solving -2(x - 3) < 18?

• X < -6

• X > 6

• X > -6

• X < 6

What does an open circle on a number line represent?

• The number is included in the solution

• The number is not included in the solution

• The number is the only solution

• The number is a placeholder

If the inequality was X ≥ -6, how would the graph change?

• The circle would be open at -6

• The graph would not change

• The circle would be closed at -6

• The arrow would point to the left

Which direction does the arrow point for the inequality X > -6?

• To the left

• To the right

• Upwards

• Downwards

Why might someone prefer to graph the solution above the number line?

• It is more accurate

• It is a requirement

• It is a standard practice

• It is easier to see

What does the final graph tell us about the values of X?

• X can be any number less than -6

• X can be any number greater than -6

• X can be any number

• X can only be -6