Question

does the equation 4(x - 2) = 4x - 6 have one solution, no solutions, or infinitely many solutions?
4(x - 2) = 4x - 6
4x - \square = 4x - 6

Explanation:

Step1: Expand left-hand side

$4(x-2) = 4x - 8$

Step2: Compare to right-hand side

Set equal to $4x-6$: $4x - 8 = 4x - 6$

Step3: Simplify to check solutions

Subtract $4x$ from both sides: $-8 = -6$

Answer:

First, fill the box with 8. The simplified equation results in a false statement ($-8=-6$), so the equation has no solutions.