Understanding Inequalities and Solutions

The video tutorial explores whether the ordered pairs (3, 5) and (1, -7) are solutions to the inequality 5x - 3y ≥ 25. The instructor tests each pair by substituting the values into the inequality. The pair (3, 5) does not satisfy the inequality, while (1, -7) does. The tutorial then demonstrates how to graph the inequality, converting it into slope-intercept form and identifying the solution region. The graph helps visualize why (3, 5) is not a solution and (1, -7) is, as it lies within the solution area.

What is the inequality we are trying to solve in this problem?

• 5x + 3y ≤ 25

• 5x + 3y ≥ 25

• 5x - 3y ≥ 25

• 5x - 3y ≤ 25

What is the first step in testing the ordered pair (3, 5)?

• Transform the inequality into slope-intercept form

• Graph the inequality

• Substitute x = 3 and y = 5 into the inequality

• Substitute x = 5 and y = 3 into the inequality

What is the result of substituting x = 3 and y = 5 into the inequality?

• 25 ≥ 25

• 0 ≥ 25

• 15 ≥ 25

• 30 ≥ 25

Why is the ordered pair (3, 5) not a solution to the inequality?

• Because 25 is not greater than or equal to 25

• Because 30 is not greater than or equal to 25

• Because 15 is not greater than or equal to 25

• Because 0 is not greater than or equal to 25

What is the result of substituting x = 1 and y = -7 into the inequality?

• 5 + 21 ≥ 25

• 5 - 21 ≥ 25

• 5 + 21 ≤ 25

• 5 - 21 ≤ 25

What is the final result of 5 + 21 in the context of the inequality?

• 26 is not a valid result

• 26 is equal to 25

• 26 is less than 25

• 26 is indeed greater than or equal to 25

What happens to the inequality sign when both sides are divided by a negative number?

• It swaps direction

• It becomes undefined

• It becomes an equality

• It remains the same

What is the slope-intercept form of the inequality 5x - 3y ≥ 25?

• y ≥ -5/3x + 25/3

• y ≤ -5/3x + 25/3

• y ≥ 5/3x - 25/3

• y ≤ 5/3x - 25/3

Where is the y-intercept of the line y = 5/3x - 25/3?

• At 25/3

• At -25/3

• At 8 and 1/3

• At -8 and 1/3

Which region represents the solution to the inequality y ≤ 5/3x - 25/3?

• Below the line

• On the line

• None of the above

• Above the line