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The point \( (5, 3) \) satisfies the inequality \( x - y \geq 2 \).
Solución
To solve the inequality \( x - y \geq 2 \) and check if the point \( (5, 3) \) satisfies it, we can follow these steps:
1. **Substitute the point into the inequality**: We will replace \( x \) with 5 and \( y \) with 3 in the inequality.
2. **Evaluate the inequality**: We will check if the resulting expression holds true.
Let's perform the substitution and evaluation:
\[
x - y \geq 2 \implies 5 - 3 \geq 2
\]
Now, we calculate:
\[
5 - 3 = 2
\]
So, we have:
\[
2 \geq 2
\]
This statement is true. Therefore, the point \( (5, 3) \) satisfies the inequality \( x - y \geq 2 \).
In conclusion, the point \( (5, 3) \) is a solution to the inequality \( x - y \geq 2 \).
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Simplifique esta solución Bonus Knowledge
The inequality \( x - y \geq 2 \) represents a region on a graph where, for any point \((x, y)\), the value of \(x\) is at least 2 units greater than \(y\). This means if you draw the line \(x - y = 2\), the area above and to the right of this line is part of the solution set. The point \( (5, 3) \) lies in this region because \(5 - 3 = 2\), which satisfies the inequality! To visualize and work with inequalities like this effectively, a common mistake is to forget that the inequality \( \geq \) means that points on the line itself are included in the solution set. Always remember to shade the correct side of the line on the graph to represent all possible solutions properly!
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