Verified Answer :

  • The point is \((-8, 5)\), so the x-coordinate is \(-8\).
  • The condition to satisfy is \(x \geq 3\).
  • Substituting \(-8\) for \(x\) results in \(-8 \geq 3\), which is a false statement.
  • The point does not satisfy the inequality, so the answer is \(\boxed{b}\).

Explanation

  1. Analysis of the point and the inequality

The problem asks whether the point \((-8, 5)\) satisfies the inequality \(x \geq 3\). An ordered pair \((x, y)\) represents a point on the Cartesian plane where the first value is the x-coordinate and the second is the y-coordinate. For the given point \((-8, 5)\), we have \(x = -8\) and \(y = 5\). The inequality is given in terms of \(x\) only, which means the condition must hold true for the x-coordinate of the point.

  1. Substitution of the x-coordinate

To check if the point satisfies the inequality, we substitute the x-coordinate of the point, which is \(-8\), into the inequality \(x \geq 3\). This gives us the expression \(-8 \geq 3\).

  1. Evaluation and conclusion

Now we evaluate the inequality \(-8 \geq 3\). Since \(-8\) is to the left of \(3\) on the number line, it is clearly less than \(3\). Therefore, the statement \(-8 \geq 3\) is false. Consequently, the point \((-8, 5)\) does not satisfy the inequality \(x \geq 3\). The answer to the question is 'no'.

Examples

In navigation or game design, you often need to define regions on a map. For example, if a "restricted zone" is defined by all points where the x-coordinate is \(x \geq 3\), a player at position \((-8, 5)\) would be safely outside this zone. Understanding how to check points against inequalities helps in determining whether an object or person is within specific boundaries on a grid or graph.

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