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Let's solve this inequality: 

### Given inequality:
\[
y \geq 2x - 1
\]

### We need to check which of the given points satisfies this inequality. 

#### Option A: \( (4, 2) \)

Substitute \( x = 4 \) and \( y = 2 \) into the inequality:
\[
2 \geq 2(4) - 1
\]
\[
2 \geq 8 - 1
\]
\[
2 \geq 7 \quad \text{(false)}
\]
So, option A is **not** a solution.

#### Option B: \( (4, 1) \)

Substitute \( x = 4 \) and \( y = 1 \):
\[
1 \geq 2(4) - 1
\]
\[
1 \geq 8 - 1
\]
\[
1 \geq 7 \quad \text{(false)}
\]
So, option B is **not** a solution.

#### Option C: \( (0, -10) \)

Substitute \( x = 0 \) and \( y = -10 \):
\[
-10 \geq 2(0) - 1
\]
\[
-10 \geq -1 \quad \text{(false)}
\]
So, option C is **not** a solution.

#### Option D: \( (0, 2) \)

Substitute \( x = 0 \) and \( y = 2 \):
\[
2 \geq 2(0) - 1
\]
\[
2 \geq -1 \quad \text{(true)}
\]
So, option D **is** a solution.

### Final Answer: 
The correct solution is **D. (0, 2)**.

Would you like further details on solving inequalities or have any other questions? 

Here are 5 related questions to explore:
1. How do you graph the inequality \( y \geq 2x - 1 \)?
2. How do you determine if a point lies on the boundary line of an inequality?
3. What is the difference between \( y \geq 2x - 1 \) and \( y > 2x - 1 \)?
4. How do inequalities change when multiplying by a negative number?
5. How can we test points to check if they satisfy a system of inequalities?

**Tip:** Always test points by substituting them directly into the inequality to check if they satisfy the condition!

Which point is a solution to y ≥ 2x - 1?

Discover which point satisfies the linear inequality y ≥ 2x - 1. This step-by-step solution explores how to substitute points into the inequality to check for validity. Ideal for students in Grades 7-9.

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