Solving and Graphing Inequalities: A Comprehensive Guide

The video tutorial covers the basics of inequalities, including how to solve and graph them. It explains the use of open and closed circles in graphing, the rules for solving inequalities, and the importance of flipping the inequality sign when multiplying or dividing by a negative number. The tutorial also provides several example problems with step-by-step solutions to reinforce the concepts.

What does an open circle on a number line represent in inequalities?

• The number is irrelevant to the solution.

• The number is both included and not included.

• The number is not included in the solution.

• The number is included in the solution.

Which symbol is used to represent 'greater than or equal to'?

• ≥

• ≤

• >

• <

How do you graph x > 3 on a number line?

• Closed circle on 3, pointing to the right.

• Open circle on 3, pointing to the right.

• Closed circle on 3, pointing to the left.

• Open circle on 3, pointing to the left.

What does a closed circle on a number line indicate?

• The number is both included and not included.

• The number is irrelevant to the solution.

• The number is included in the solution.

• The number is not included in the solution.

How can you remember the 'less than' symbol?

• It looks like a squished 'E'.

• It looks like a squished 'G'.

• It looks like a squished 'L'.

• It looks like a squished 'S'.

What must you do when you multiply or divide both sides of an inequality by a negative number?

• Add a negative sign to the inequality symbol.

• Flip the inequality symbol.

• Remove the inequality symbol.

• Keep the inequality symbol the same.

Solve the inequality: 3x + 2 < 8. What is x?

• x < 2

• x > 2

• x ≤ 2

• x ≥ 2

What is the solution to the inequality: -2x + 5 ≤ 8?

• x > -3/2

• x < -3/2

• x ≤ -3/2

• x ≥ -3/2

How do you graph x > 0 on a number line?

• Closed circle on 0, pointing to the right.

• Open circle on 0, pointing to the right.

• Open circle on 0, pointing to the left.

• Closed circle on 0, pointing to the left.

Solve the inequality: 4x + 13 > 9. What is x?

• x ≥ -1

• x > -1

• x ≤ -1

• x < -1