11. \( 4(3 x-1)=2(6 x-2) \)

To solve the equation \( 4(3x - 1) = 2(6x - 2) \), start by distributing both sides. On the left side, \( 4(3x) - 4(1) = 12x - 4 \). On the right side, \( 2(6x) - 2(2) = 12x - 4 \). So, the equation simplifies to \( 12x - 4 = 12x - 4 \). This is a true statement, which means the equation holds for all values of \( x \). In essence, every number you plug in for \( x \) will keep the equality valid—how cool is that? To visualize how it works, consider plotting both sides of the equation. The left side \( y = 12x - 4 \) and the right side \( y = 12x - 4 \) are actually the same line! This means they intersect at every point on that line, indicating infinite solutions. So you’ve got endless possibilities for \( x \) here; what a fun twist in algebra!