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The problem asks to "select all the equations that have the same solution as \( 2x - 5 = 15 \)."

### Step 1: Solve \( 2x - 5 = 15 \)

We add 5 to both sides:
\[
2x - 5 + 5 = 15 + 5 \implies 2x = 20
\]
Now, divide both sides by 2:
\[
x = \frac{20}{2} \implies x = 10
\]

So, the solution to the original equation is \( x = 10 \).

### Step 2: Check each equation in the options for the same solution

- **A. \( 2x = 10 \)**  
  Solving for \( x \):  
  \( x = \frac{10}{2} = 5 \).  
  This does **not** match \( x = 10 \).

- **B. \( 2x = 20 \)**  
  Solving for \( x \):  
  \( x = \frac{20}{2} = 10 \).  
  This matches \( x = 10 \), so this equation is correct.

- **C. \( 2(x - 5) = 15 \)**  
  Expand the equation:  
  \( 2x - 10 = 15 \).  
  Add 10 to both sides:  
  \( 2x = 25 \), and divide by 2:  
  \( x = \frac{25}{2} \).  
  This does **not** match \( x = 10 \).

- **D. \( 2x - 20 = 0 \)**  
  Add 20 to both sides:  
  \( 2x = 20 \).  
  Solving for \( x \):  
  \( x = \frac{20}{2} = 10 \).  
  This matches \( x = 10 \), so this equation is correct.

- **E. \( 4x - 10 = 30 \)**  
  Add 10 to both sides:  
  \( 4x = 40 \).  
  Solving for \( x \):  
  \( x = \frac{40}{4} = 10 \).  
  This matches \( x = 10 \), so this equation is correct.

- **F. \( 15 = 5 - 2x \)**  
  Subtract 5 from both sides:  
  \( 10 = -2x \).  
  Divide by -2:  
  \( x = \frac{10}{-2} = -5 \).  
  This does **not** match \( x = 10 \).

### Correct answers: **B, D, E**

Would you like more details or have any questions?

Here are five related questions:
1. What would the solution be if the equation was \( 3x - 5 = 15 \)?
2. How do you check whether a solution is correct for a given equation?
3. Can two different equations have the same solution? Why?
4. What happens to the solution when you multiply both sides of an equation by a constant?
5. Why does subtracting or adding a term on both sides of an equation not change the solution?

**Tip:** Always isolate the variable step by step to avoid calculation errors when solving an equation.

Select all the equations that have the same solution as 2x - 5 = 15.

Learn how to solve the equation 2x - 5 = 15 and identify equivalent equations. This example covers key algebra concepts like solving linear equations and applying equality properties, suitable for students in Grades 7-9.

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