b) \( 2 x+1=x+(-6) \)

To solve the equation \( 2x + 1 = x + (-6) \), we start by simplifying it. Combining like terms gives us \( 2x + 1 = x - 6 \). Next, we move \( x \) from the right side to the left side by subtracting \( x \) from both sides. This results in \( 2x - x + 1 = -6 \), which simplifies to \( x + 1 = -6 \). Subtracting 1 from both sides, we find \( x = -7 \). To verify our solution, we can substitute \( x = -7 \) back into the original equation. The left side becomes \( 2(-7) + 1 = -14 + 1 = -13 \), and the right side becomes \( -7 + (-6) = -7 - 6 = -13 \). Since both sides are equal, \( x = -7 \) is indeed the correct solution!