Question

Determine whether each ordered pair is a solution of the inequality: -3x - 4y < 6.

A. (1, -2)
B. (6, 0)
C. (2, -1)
D. (-1, -1)

Answer 1

Ordered pairs A (1, -2), B (6, 0), and C (2, -1) are solutions to the inequality -3x - 4y < 6, as the substitutions yield true inequalities. However, ordered pair D (-1, -1) is not a solution because the substitution results in a false inequality.

Step-by-step explanation:

To determine whether each ordered pair is a solution of the inequality -3x - 4y < 6, we must substitute the x and y values from each pair into the inequality and check if the inequality holds.

1. For the ordered pair A. (1, -2), the inequality becomes -3(1) - 4(-2) < 6, which simplifies to -3 + 8 < 6. Since 5 < 6 is true, pair A is a solution.
2. For the ordered pair B. (6, 0), the inequality becomes -3(6) - 4(0) < 6, which simplifies to -18 < 6. This is true, so pair B is also a solution.
3. For the ordered pair C. (2, -1), the inequality becomes -3(2) - 4(-1) < 6, which simplifies to -6 + 4 < 6. Since -2 < 6 is true, pair C is a solution.
4. Finally, for the ordered pair D. (-1, -1), the inequality becomes -3(-1) - 4(-1) < 6, which simplifies to 3 + 4 < 6. Since 7 < 6 is false, pair D is not a solution.

In conclusion, ordered pairs A, B, and C are solutions to the inequality, whereas ordered pair D is not.