Graphing Inequalities and Number Lines

Mrs. C introduces solving and graphing inequalities, explaining the difference between equations and inequalities. She provides examples with different inequality symbols, demonstrating how to solve and graph each one. The video covers inequalities with greater than, less than, and their equal counterparts, using both whole numbers and fractions. Mrs. C emphasizes the importance of correctly interpreting the inequality symbols and graphing them accurately on a number line. The video concludes with a preview of the next lesson on solving inequalities using multiplication and division.

What is the main difference between an equation and an inequality?

• An inequality uses an equal sign.

• An inequality always has a variable on the left side.

• An equation uses an equal sign, while an inequality uses symbols like > or <.

• An equation uses symbols like > or <.

If x - 3 > -7, what is the solution for x?

• x < -4

• x ≤ -4

• x > -4

• x = -4

How do you represent x > -4 on a number line?

• Closed circle at -4 with an arrow pointing right

• Open circle at -4 with an arrow pointing left

• Open circle at -4 with an arrow pointing right

• Closed circle at -4 with an arrow pointing left

What does a closed circle on a number line indicate?

• The number is not included in the solution.

• The number is included in the solution.

• The inequality is incorrect.

• The solution is less than the number.

For the inequality w ≥ 12, which of the following is true?

• w can be 12 or any number less than 12.

• w can be 12 or any number greater than 12.

• w can be any number greater than 12.

• w can be any number less than 12.

How do you graph H < 9.5 on a number line?

• Open circle at 9.5 with an arrow pointing right

• Open circle at 9.5 with an arrow pointing left

• Closed circle at 9.5 with an arrow pointing right

• Closed circle at 9.5 with an arrow pointing left

What is the solution for r + 4 ≤ 14?

• r ≥ 10

• r ≤ 10

• r > 10

• r < 10

When solving T ≥ 1.75, what is the correct graph representation?

• Open circle at 1.75 with an arrow pointing right

• Closed circle at 1.75 with an arrow pointing right

• Closed circle at 1.75 with an arrow pointing left

• Open circle at 1.75 with an arrow pointing left

What common mistake do students make when the variable is on the right side of an inequality?

• They forget to include the variable in the solution.

• They always draw the arrow pointing right.

• They always draw the arrow pointing left.

• They forget to reverse the inequality sign.

In the inequality -37 < B, what is the correct graph representation?

• Closed circle at -37 with an arrow pointing left

• Open circle at -37 with an arrow pointing left

• Closed circle at -37 with an arrow pointing right

• Open circle at -37 with an arrow pointing right