Inequalities and Absolute Value Concepts

The video tutorial covers the basics of inequalities, including how to solve them and graph them on a coordinate plane. It also introduces absolute value, explaining how to solve equations involving absolute values. The tutorial concludes with examples that combine both inequalities and absolute values, demonstrating how to solve these complex problems.

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

• An equation can only have one variable, while an inequality can have multiple.

• An equation is always true, while an inequality is sometimes false.

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

• An equation has a solution, while an inequality does not.

When solving inequalities, what operation requires you to flip the inequality sign?

• Dividing by a positive number

• Multiplying by a negative number

• Subtracting a negative number

• Adding a positive number

How do you graph an inequality on a number line?

• Use a solid line for < or > and a dashed line for ≤ or ≥.

• Use a dashed line for < or > and a solid line for ≤ or ≥.

• Use a solid line for all inequalities.

• Use a dashed line for all inequalities.

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

• It flips direction.

• It stays the same.

• It disappears.

• It becomes an equal sign.

How do you graph the inequality y > 2x - 5?

• Shade to the right of the line y = 2x - 5.

• Shade to the left of the line y = 2x - 5.

• Shade above the line y = 2x - 5.

• Shade below the line y = 2x - 5.

What is the effect of multiplying both sides of an inequality by a negative number?

• The inequality sign remains unchanged.

• The inequality sign flips direction.

• The inequality becomes an equation.

• The inequality sign disappears.

What is the graph of the inequality y < 2x - 5?

• A dashed line with shading below

• A solid line with shading above

• A dashed line with shading above

• A solid line with shading below

What is the solution to the inequality -2x + 3 ≥ 7?

• x ≤ -2

• x ≤ 2

• x ≥ -2

• x ≥ 2

What is the solution to the inequality 3x - 4 > 5?

• x > 1

• x < 3

• x > 3

• x < 1

What is the solution to the inequality 2x + 5 ≤ 9?

• x ≥ -2

• x ≤ -2

• x ≥ 2

• x ≤ 2