Understanding and Solving Inequalities

The video tutorial explains how to solve and graph linear inequalities, emphasizing the importance of reversing the inequality symbol when multiplying or dividing by a negative number. It provides two examples: solving 2X + 8 > 16 and -4X ≥ -6, demonstrating how to express solutions as inequalities, graphs, and in interval notation.

What must you do to the inequality symbol when you multiply or divide both sides of an inequality by a negative number?

• Subtract a minus sign

• Reverse it

• Keep it the same

• Add a plus sign

What is the first step in solving the inequality 2x + 8 > 16?

• Add 8 to both sides

• Subtract 8 from both sides

• Multiply both sides by 2

• Divide both sides by 2

How do you represent that a number is not included in an interval on a graph?

• Use a square bracket

• Use a dashed line

• Use a closed point

• Use an open point

What is the interval notation for the solution x > 4?

• (4, ∞)

• [4, ∞)

• (4, ∞]

• [4, ∞]

In the second example, what operation is performed first to isolate x?

• Multiply both sides by -4

• Subtract 4 from both sides

• Add 4 to both sides

• Divide both sides by -4

What happens to the inequality symbol when dividing both sides by a negative number in the second example?

• It becomes a minus sign

• It becomes a plus sign

• It stays the same

• It reverses

What is the decimal equivalent of the fraction 3/2?

• 2.5

• 2.0

• 1.5

• 1.2

How is the number 3/2 represented on the graph for the second inequality?

• With a square bracket

• With an open point

• With a closed point

• With a dashed line

What is the interval notation for the solution x ≤ 3/2?

• (-∞, 3/2)

• (-∞, 3/2]

• [3/2, ∞)

• (3/2, ∞)

What are the three ways to express the solution of an inequality?

• As an inequality, a graph, and interval notation

• As a graph, an equation, and a table

• As a graph, a table, and a chart

• As a graph, a chart, and interval notation