4,-7 Solve vert x-12vert -3=11 -2,-26 3,25 -2,26

To solve the equation $\vert x-12\vert -3=11$, we first isolate the absolute value expression by adding 3 to both sides of the equation:<br /><br />$\vert x-12\vert -3 + 3 = 11 + 3$<br /><br />$\vert x-12\vert = 14$<br /><br />Next, we consider the two cases for the absolute value expression:<br /><br />Case 1: $x-12 \geq 0$<br /><br />In this case, the absolute value expression is equal to the expression inside the absolute value:<br /><br />$x-12 = 14$<br /><br />Solving for $x$, we get:<br /><br />$x = 14 + 12$<br /><br />$x = 26$<br /><br />Case 2: $x-12 < 0$<br /><br />In this case, the absolute value expression is equal to the negative of the expression inside the absolute value:<br /><br />$-(x-12) = 14$<br /><br />Solving for $x$, we get:<br /><br />$-x + 12 = 14$<br /><br />$-x = 14 - 12$<br /><br />$-x = 2$<br /><br />$x = -2$<br /><br />Therefore, the solutions to the equation $\vert x-12\vert -3=11$ are $x = 26$ and $x = -2$.