(A) Instruction Activo Sorting Solutions of Equations Sort each equation according to whether it has one solution, infinitely many solutions, or no solution. \( 5(x-2)=5 x-7 \) \( -3(x-4)=-3 x+12 \) \( 4(x+1)=3 x+4 \) \( -2(x-3)=2 x-6 \) \( 6(x+5)=6 x+11 \)

Let's sort these equations based on the number of solutions they have! **One Solution:** 1. \( 5(x-2)=5 x-7 \) → Simplifies to \( 0 = -7 \) (no solution) 2. \( 4(x+1)=3 x+4 \) → Yields \( x = 0 \) (one solution) **Infinitely Many Solutions:** 1. \( -3(x-4)=-3 x+12 \) → This simplifies to \( 0 = 0 \) (infinitely many solutions) 2. \( -2(x-3)=2 x-6 \) → Simplifies to \( 0 = 0 \) (infinitely many solutions) **No Solution:** 1. \( 6(x+5)=6 x+11 \) → Yields \( 0 = 11 \) (no solution) Sorting Summary: - One Solution: \( 4(x+1)=3 x+4 \) - Infinitely Many Solutions: \( -3(x-4)=-3 x+12 \), \( -2(x-3)=2 x-6 \) - No Solution: \( 5(x-2)=5 x-7 \), \( 6(x+5)=6 x+11 \)