Question

What equations have the same solution as 2x - 5 = 15?

A. 2x = 10
B. 2x = 20
C. 2(x - 5) = 15
D. 2x - 20 = 0
E. 4x - 10 = 30
F. 15 = 5 - 2x​

Answer 1

Equations B (2x = 20) and D (2x - 20 = 0) have the same solution as the given equation 2x - 5 = 15, which is x = 10.

Step-by-step explanation:

The question asks which equations have the same solution as 2x - 5 = 15. To find equations with the same solution, one must manipulate the given equation algebraically without changing its solution set.

First, let's solve the given equation:

• Add 5 to both sides: 2x = 20.
• Divide both sides by 2: x = 10.

Now, we compare this process with the provided options:

• Option B: Directly states 2x = 20, which has the same solution as the given equation.
• Option D: Rearranging gives 2x = 20 after adding 20, which is the same as the given equation's solution.
• Option F: Rearranging gives 2x = 5 - 15 which simplifies to 2x = -10. This does not match the solution to the given equation.

The correct equations with the same solution as 2x - 5 = 15 are options B and D.