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Which of these ordered pairs is a solution to the inequality y-2x < -3? -

(12, 4) - (-2, 3) - (3, 4) - (1, -1)

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Final answer:

The ordered pair (12, 4) is a solution to the inequality y - 2x < -3, as it satisfies the inequality when substituted, resulting in -20 < -3, which is true.

Step-by-step explanation:

To determine which of the given ordered pairs is a solution to the inequality y - 2x < -3, we must substitute the x and y values from each pair into the inequality and check if the inequality holds true.

  • For the pair (12, 4), if we substitute x = 12 and y = 4, we get 4 - 2(12) = 4 - 24, which simplifies to -20, yielding -20 < -3, which is true, meaning this pair is a solution.
  • Checking the pair (-2, 3), substituting x = -2 and y = 3 gives us 3 - 2(-2) = 3 + 4, which simplifies to 7, yielding 7 < -3, which is false, so this pair is not a solution.
  • For the pair (3, 4), substituting x = 3 and y = 4 gives us 4 - 2(3) = 4 - 6, which simplifies to -2, yielding -2 < -3, which is false, showing this pair is not a solution.
  • Lastly, for the pair (1, -1), substituting x = 1 and y = -1 gives us -1 - 2(1) = -1 - 2, which simplifies to -3, yielding -3 < -3, which is false as the inequality must be strictly less than, indicating this pair is not a solution as well.

So, the ordered pair that satisfies the inequality y - 2x < -3 is (12, 4).

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