We are tasked with determining if the point $(2, 10)$ is a solution to the inequality $y > 5x - 2$.

Step 1: Substitute $x = 2$ and $y = 10$ into the inequality.

The inequality is $y > 5x - 2$.

Substitute $x = 2$ and $y = 10$ into the inequality:

$10 > 5(2) - 2$

Step 2: Simplify the right-hand side.

$10 > 10 - 2$ $10 > 8$

Step 3: Check if the inequality holds true.

Since $10 > 8$ is true, the point $(2, 10)$ satisfies the inequality.

Conclusion:

Yes, $(2, 10)$ is a solution to the inequality $y > 5x - 2$.

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If you would like further clarification or details, feel free to ask!

Here are five related questions you may find interesting:

1. How do you graph the inequality $y > 5x - 2$?
2. How would the solution change if the inequality were $y \geq 5x - 2$?
3. What happens if the point is on the boundary line $y = 5x - 2$?
4. How do you test a point for inequalities with "less than" instead of "greater than"?
5. What is the significance of the slope and y-intercept in graphing inequalities?

Tip: When solving inequalities, always test points carefully by substitution to verify whether they satisfy the inequality!