Solving and Graphing Inequalities

This video tutorial covers the basics of solving inequalities, including properties and graphing techniques. It explains how to solve inequalities using addition, subtraction, multiplication, and division, and how to graph the solutions on a number line. The tutorial also includes examples of both simple and multi-step inequalities, demonstrating how to isolate variables and determine the direction of shading on a graph.

What happens to the inequality sign when you add the same number to both sides of an inequality?

• The inequality sign flips.

• The inequality sign disappears.

• The inequality sign remains unchanged.

• The inequality sign becomes an equal sign.

When multiplying both sides of an inequality by a negative number, what must you do to the inequality sign?

• Leave it unchanged.

• Flip it.

• Change it to an equal sign.

• Remove it.

What type of circle is used on a number line to represent a 'less than' inequality?

• No circle

• Half-filled circle

• Open circle

• Closed circle

In graphing inequalities, what does a closed circle represent?

• The inequality is strict.

• The endpoint is included.

• The endpoint is not included.

• The inequality is invalid.

How do you isolate the variable in the inequality X - 15 > -12?

• Subtract 15 from both sides.

• Add 15 to both sides.

• Divide both sides by 15.

• Multiply both sides by 15.

What is the solution to the inequality 13 ≥ X rewritten with X on the left side?

• X ≤ 13

• X ≥ 13

• X < 13

• X > 13

When solving the inequality -5y < 10, what must you do to the inequality sign after dividing by -5?

• Change it to an equal sign.

• Remove it.

• Flip it.

• Leave it unchanged.

In the inequality 6n - 1 ≥ 3n + 8, what is the first step to isolate the variable n?

• Add 1 to both sides.

• Subtract 3n from both sides.

• Divide both sides by 6.

• Multiply both sides by 3.

What is the solution to the inequality -3x - 9 + 9x < -15 after combining like terms?

• 6x < 6

• 6x < -6

• 6x < -15

• 6x < 15

When solving the inequality 6 - 3x ≤ 5x + 4 - x, what should you do first?

• Subtract 4 from both sides.

• Divide both sides by 5.

• Add 3x to both sides.

• Combine like terms on the right side.