1. **State the problem:** We need to determine which of the given equations have exactly one solution. 2. **Recall:** An equation has one solution if it simplifies to a linear equation with a unique value for $x$. 3. **Analyze each equation:** **A.** $2x + 2x + 2 = 4x + 2$ Simplify left side: $4x + 2 = 4x + 2$ Subtract $4x + 2$ from both sides: $0 = 0$ This means infinitely many solutions, not one. **B.** $\frac{3}{4}(4x - 8) = 18$ Distribute: $3x - 6 = 18$ Add 6: $3x = 24$ Divide by 3: $x = 8$ One unique solution. **C.** $x + x - (x + x) = 2x - x + 2$ Simplify left: $2x - 2x = 0$ Simplify right: $x + 2$ Equation: $0 = x + 2$ Solve: $x = -2$ One unique solution. **D.** $\frac{1}{2}x = x + \frac{1}{2}$ Bring all terms to one side: $\frac{1}{2}x - x = \frac{1}{2}$ Simplify: $-\frac{1}{2}x = \frac{1}{2}$ Multiply both sides by $-2$: $x = -1$ One unique solution. **E.** $-3(-x - 2) = 3(x - 2)$ Distribute left: $3x + 6 = 3x - 6$ Subtract $3x$: $6 = -6$ False statement, no solution. 4. **Conclusion:** Equations B, C, and D have exactly one solution. **Final answer:** B, C, D