\( \frac{3}{8} x-2=\frac{1}{8}(3 x-16) \) one solution no solution infinitely many solutions two solutions

To solve the equation \( \frac{3}{8} x - 2 = \frac{1}{8}(3 x - 16) \), start by simplifying both sides. Distributing on the right side gives \( \frac{3}{8} x - 2 = \frac{3}{8} x - 2 \). When you bring all terms to one side, you get \( 0 = 0 \). This means every value of \( x \) satisfies the equation, leading us to conclude that there are infinitely many solutions! It’s a neat aspect of algebra that sometimes, instead of finding a single solution or a conflict, you can discover that an equation is true for all possible values of the variable. This happens when the two sides of the equation are identical after simplification—an algebraic harmony!