Understanding Inequalities

The video tutorial explains how to solve inequalities, highlighting the key difference from equations: flipping the inequality sign when multiplying or dividing by a negative number. It provides three examples: solving inequalities using addition, handling inequalities with 'less than or equal to', and solving inequalities involving multiplication and division. Each example includes graphing the solution on a number line, demonstrating open and closed circles for strict and inclusive inequalities, respectively.

What is the main difference between solving equations and inequalities?

• You always add numbers to both sides in inequalities.

• Equations always have more than one solution.

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

• Inequalities do not require graphing.

In the first example, what operation is used to isolate the variable?

• Addition

• Division

• Subtraction

• Multiplication

How is the solution graphed when the inequality is 'less than'?

• Draw an open circle and shade to the left.

• Draw a filled circle and shade to the right.

• Draw an open circle and shade to the right.

• Draw a filled circle and shade to the left.

What is the key difference in the second example compared to the first?

• The solution is shaded to the right.

• The variable is on the right side.

• The inequality includes an 'equal to' condition.

• The inequality sign is flipped.

How is the graph different when the inequality includes 'equal to'?

• Use a dashed line.

• Draw an open circle.

• Shade above the line.

• Draw a filled circle.

In the third example, what operation requires flipping the inequality sign?

• Multiplying by a negative number

• Dividing by a positive number

• Subtracting a negative number

• Adding a positive number

What is the result of dividing 21 by negative 5 in the third example?

• x is equal to 4 and 1 fifth

• x is less than or equal to negative 4 and 1 fifth

• x is greater than or equal to negative 4 and 1 fifth

• x is greater than 4 and 1 fifth