Understanding Inequalities and Their Graphs

The video tutorial explains how to solve and graph combined inequalities. It starts by solving each individual inequality for X, ensuring to switch the inequality sign when dividing by a negative number. The solutions are then graphed on a number line, with closed and open dots representing the inequalities. Finally, the video demonstrates how to combine the inequalities using union to find the overall solution.

What is the first step in solving a combined inequality?

• Graph the inequalities

• Solve each inequality separately

• Combine the inequalities immediately

• Ignore one of the inequalities

When distributing -3 in the first inequality, what expression do we get?

• 5 - 6x + 3

• 5 + 6x - 3

• 5 - 6x - 3

• 5 - 3x - 3

What is the first step in solving the inequality on the left?

• Multiply both sides by 3

• Subtract 5 from both sides

• Distribute -3 through the parentheses

• Add 3 to both sides

After simplifying the left side of the first inequality, what expression do we have?

• 2 - 6X is greater than or equal to 14

• 2 + 6X is greater than or equal to 14

• 2 - 6X is less than or equal to 14

• 2 + 6X is less than or equal to 14

What must you remember when dividing both sides of an inequality by a negative number?

• The inequality sign is removed

• The inequality becomes an equation

• The inequality sign switches direction

• The inequality sign stays the same

What is the result of combining the X terms in the second inequality?

• 5x is less than or equal to 15

• 5x is equal to 15

• 5x is greater than 15

• 5x is less than 15

What is the result of subtracting 4X from both sides in the second inequality?

• 5x is less than 15

• 5x is equal to 15

• 5x is less than or equal to 15

• 5x is greater than 15

How is the inequality X < 3 represented on a number line?

• Closed dot at 3 with an arrow to the right

• Open dot at 3 with an arrow to the left

• Closed dot at 3 with an arrow to the left

• Open dot at 3 with an arrow to the right

What does a closed dot on a number line indicate?

• The number is not included in the solution

• The number is included in the solution

• The number is a boundary but not included

• The number is irrelevant to the solution

What does an open dot on a number line indicate?

• The number is included in the solution

• The number is not included in the solution

• The number is a boundary and included

• The number is irrelevant to the solution