Exploring Inequalities in One Variable

The video tutorial covers solving and graphing inequalities. It explains the difference between inequalities and equalities, and provides step-by-step examples of solving inequalities such as x < 4, V < -5, and x ≤ -2. The tutorial emphasizes the importance of flipping the inequality sign when dividing by a negative number and demonstrates how to graph the solution sets on a number line. The session concludes with instructions for classwork and homework.

What is an inequality?

• A mathematical statement that shows two expressions are not equal.

• A mathematical statement that shows one expression is greater than or less than another.

• A mathematical statement that shows one expression is a multiple of another.

• A mathematical statement that shows two expressions are equal.

Which of the following is a correct representation of the inequality 2x < 8?

• x <= 4

• x > 4

• x < 4

• x >= 4

How do you represent the solution of x < 4 on a graph?

• A closed circle at 4 and shading to the left.

• An open circle at 4 and shading to the right.

• A closed circle at 4 and shading to the right.

• An open circle at 4 and shading to the left.

What is the first step in solving the inequality -3V + 7 > 22?

• Multiply both sides by -3.

• Subtract 7 from both sides.

• Divide both sides by -3.

• Add 7 to both sides.

What happens to the inequality sign when you divide both sides by a negative number?

• It becomes undefined.

• It becomes an equality.

• It flips.

• It stays the same.

What is the solution to the inequality -3V + 7 > 22?

• V > -5

• V < -5

• V >= -5

• V <= -5

How do you represent the solution of V > -5 on a graph?

• An open circle at -5 and shading to the left.

• An open circle at -5 and shading to the right.

• A closed circle at -5 and shading to the left.

• A closed circle at -5 and shading to the right.

What is the first step in solving the inequality -2(5x + 3) >= 14?

• Divide both sides by -2.

• Subtract 3 from both sides.

• Multiply both sides by -2.

• Add 3 to both sides.

What is the solution to the inequality -2(5x + 3) >= 14?

• x <= -2

• x > -2

• x >= -2

• x < -2

How do you represent the solution of x <= -2 on a graph?

• A closed circle at -2 and shading to the left.

• An open circle at -2 and shading to the left.

• A closed circle at -2 and shading to the right.

• An open circle at -2 and shading to the right.