Understanding Inequalities and Solutions

The video tutorial explains how to determine which X values make the ordered pair (X, -7) a solution to the inequality 2x - 7y < 25. It involves substituting Y with -7 and solving for X. The tutorial also covers determining Y values for the ordered pair (5, Y) using a graph, emphasizing that solutions lie above a dashed line, indicating Y must be greater than 7.

What is the inequality given in the problem for which we need to find the X values?

• 2x + 7y < 25

• 2x - 7y < 25

• 2x - 7y > 25

• 2x + 7y > 25

What value is y constrained to in the first problem?

• 0

• 7

• 12

• -7

After substituting y = -7, what is the simplified inequality?

• 2x - 49 > 25

• 2x + 49 > 25

• 2x - 49 < 25

• 2x + 49 < 25

What is the final solution for X in the inequality 2x + 49 < 25?

• X < -12

• X > 12

• X > -12

• X < 12

In the second problem, what is the ordered pair for which we need to find y values?

• (x, y)

• (5, y)

• (x, -7)

• (5, 7)

What does a dashed line on a graph indicate about the solutions?

• Points on the line are solutions

• Points above the line are solutions

• Points on and above the line are solutions

• Points below the line are solutions

What is the condition for y to ensure the ordered pair (5, y) is a solution?

• y ≥ 7

• y > 7

• y < 7

• y = 7

Why can't y be equal to 7 in the solution set?

• Because the line is solid

• Because y must be equal to 7

• Because the line is dashed

• Because y must be less than 7

What does it mean for a point to be a solution in the context of a graph?

• It lies below the line

• It lies above the line

• It lies on the line

• It lies on or above the line

What is the significance of the blue area in the graph?

• It represents the boundary line

• It represents the non-solution set

• It represents the axis

• It represents the solution set