Question

which of the following has exactly one solution

A. -8x + 3 = -8x + 3
B. 3x - 8 = 3x + 8
C. -3x + 8 = -3x - 8
D. -3x - 8 = 3x - 8

Answer 1

To determine which equation has exactly one solution, let's analyze each option:

A. \(-8x + 3 = -8x + 3\)

This is an identity (both sides are equal for all values of \(x\)), so it has infinitely many solutions.

B. \(3x - 8 = 3x + 8\)

Subtracting \(3x\) from both sides gives \(-8 = 8\), which is false. This has no solutions.

C. \(-3x + 8 = -3x - 8\)

Subtracting \(-3x\) from both sides gives \(8 = -8\), which is also false. This has no solutions.

D. \(-3x - 8 = 3x - 8\)

Adding \(3x\) to both sides gives \(-8 = 6x - 8\).

Adding \(8\) to both sides gives \(0 = 6x\).

Dividing by \(6\) gives \(x = 0\). This has exactly one solution.

Therefore, the answer is **D. -3x - 8 = 3x - 8**.