Solve the equation. \[ 5(-3 x+1)=-14(x+1) \]

To solve the equation \( 5(-3x + 1) = -14(x + 1) \), let's first distribute both sides. Starting with the left side: \[ 5(-3x + 1) = -15x + 5 \] Now, distribute on the right side: \[ -14(x + 1) = -14x - 14 \] Now we can rewrite the equation as: \[ -15x + 5 = -14x - 14 \] Next, we'll get all terms involving \( x \) on one side and constants on the other. We can add \( 14x \) to both sides: \[ -15x + 14x + 5 = -14 \] \[ -x + 5 = -14 \] Now, subtract \( 5 \) from both sides: \[ -x = -14 - 5 \] \[ -x = -19 \] Finally, multiply both sides by -1: \[ x = 19 \] So, the solution to the equation is \[ \boxed{19} \]