Inequalities and Their Representations

This video tutorial focuses on solving inequalities and graphing them on a number line. It begins with an introduction to inequalities, followed by several examples that demonstrate how to solve different types of inequalities, including simple and compound inequalities. Each example includes step-by-step instructions on solving the inequality and graphing the solution on a number line, with explanations on using open and closed circles and interval notation.

What is the first step in solving the inequality 2x + 3 > 7?

• Add 3 to both sides

• Divide both sides by 2

• Subtract 3 from both sides

• Multiply both sides by 2

How do you represent the solution of x > 2 on a number line?

• Open circle at 2, shade right

• Open circle at 2, shade left

• Closed circle at 2, shade left

• Closed circle at 2, shade right

What operation is used to eliminate the fraction in the inequality 1/3x + 4 ≤ 6?

• Add 3 to both sides

• Subtract 4 from both sides

• Divide both sides by 3

• Multiply both sides by 3

In the inequality x ≤ 6, how is the solution represented on a number line?

• Open circle at 6, shade right

• Closed circle at 6, shade right

• Closed circle at 6, shade left

• Open circle at 6, shade left

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

• It disappears

• It becomes an equal sign

• It changes direction

• It remains the same

How is the solution x ≤ 3 represented using interval notation?

• [3, ∞)

• (-∞, 3]

• (-∞, 3)

• [3, ∞]

In the compound inequality 2x - 1 > 7 or -3x + 2 ≥ -1, what is the solution for 2x - 1 > 7?

• x < 4

• x > 4

• x ≥ 4

• x ≤ 4

How is the solution for the compound inequality -3x + 2 ≥ -1 represented on a number line?

• Open circle at 1, shade left

• Closed circle at 1, shade left

• Closed circle at 1, shade right

• Open circle at 1, shade right

In the inequality -12 < 7x - 5 ≤ 9, what is the first step to isolate x?

• Subtract 5 from all sides

• Add 5 to all sides

• Multiply all sides by 7

• Divide all sides by 7

How is the solution for the inequality -1 < x ≤ 2 represented using interval notation?

• [-1, 2]

• (-1, 2)

• [-1, 2)

• (-1, 2]