Understanding Solutions to Inequalities

The video tutorial explains how to determine if an ordered pair is a solution to the inequality 2x + 4y ≥ 8. It demonstrates the process of substituting values into the inequality and checking if they satisfy it. The tutorial evaluates several ordered pairs, identifying which ones are solutions. Additionally, it introduces a graphical approach to visualize the solution set on a coordinate plane, highlighting the region that satisfies the inequality.

What is the first step in determining if an ordered pair is a solution to the inequality 2x + 4y ≥ 8?

• Graph the inequality on a coordinate plane.

• Calculate the slope of the line 2x + 4y = 8.

• Substitute the values of x and y into the inequality.

• Check if the ordered pair is in the first quadrant.

When substituting the ordered pair (3, 2) into the inequality 2x + 4y ≥ 8, what is the result?

• The result is less than 8.

• The result is exactly 8.

• The inequality is satisfied.

• The inequality is not satisfied.

Which of the following ordered pairs does NOT satisfy the inequality 2x + 4y ≥ 8?

• (3, 2)

• (0, 0)

• (2, 3)

• (1, 1)

What is the result when substituting the ordered pair (0, 0) into the inequality 2x + 4y ≥ 8?

• The result is exactly 8.

• The inequality is satisfied.

• The result is greater than 8.

• The inequality is not satisfied.

Why does the ordered pair (1, 1) not satisfy the inequality 2x + 4y ≥ 8?

• Because 2 + 4 is equal to 8.

• Because 2 + 4 is not a valid operation.

• Because 2 + 4 is greater than 8.

• Because 2 + 4 is less than 8.

Which ordered pair is confirmed as the only solution to the inequality 2x + 4y ≥ 8?

• (1, 0)

• (3, 2)

• (1, 1)

• (0, 0)

What is the alternative method mentioned for solving the inequality 2x + 4y ≥ 8?

• Using a calculator to solve the inequality.

• Graphing the inequality on a coordinate plane.

• Solving the inequality algebraically.

• Using a table of values.

In the graphical approach, where are the solutions to the inequality 2x + 4y ≥ 8 located?

• Below the line.

• On the line only.

• Above the line and on the line.

• To the left of the line.

What type of line is used to graph the inequality 2x + 4y ≥ 8?

• No line is used.

• A dotted line.

• A solid line.

• A dashed line.

Which point is in the shaded region when graphing the inequality 2x + 4y ≥ 8?

• (3, 2)

• (1, 1)

• (1, 0)

• (0, 0)