Question

Which of the following mathematical sentences has only one solution?

A) x + 3 = 7
B) 2x - 5 = x + 3
C) 4(x - 2) = 2x + 6
D) 3(x - 4) = 2(x + 1)

Answer 1

The mathematical sentence that has only one solution is A) x + 3 = 7.

Step-by-step explanation:

To determine which of the given mathematical sentences has only one solution, we need to solve each equation and see how many distinct values the variable 'x' can have.

1. A) x + 3 = 7
   Solution: Subtracting 3 from both sides gives us x = 4. This equation has only one solution.
2. B) 2x - 5 = x + 3
   Solution: Subtracting x from both sides gives us x - 5 = 3, and adding 5 to both sides gives us x = 8. This equation has only one solution.
3. C) 4(x - 2) = 2x + 6
   Solution: Distributing 4 gives us 4x - 8 = 2x + 6. Subtracting 2x from both sides gives us 2x - 8 = 6, and adding 8 to both sides gives us 2x = 14. Dividing both sides by 2 gives us x = 7. This equation has only one solution.
4. D) 3(x - 4) = 2(x + 1)
   Solution: Distributing 3 gives us 3x - 12 = 2x + 2. Subtracting 2x from both sides gives us x - 12 = 2, and adding 12 to both sides gives us x = 14. This equation has only one solution.

Based on the above solutions, the mathematical sentence A) x + 3 = 7 has only one solution.