Johan found that the equation -2vert 8-xvert -6=-12 had two possible solutions: x=5 and x=-11 Which explains whether his solutions are correct? He is correct because both solutions satisfy the equation. He is not correct because he made a sign error. He is not correct because there are no solutions. He is not correct because there is only one solution: x=5.

To determine whether Johan's solutions are correct, we need to substitute each solution into the equation and see if it satisfies the equation.<br /><br />Let's start with the first solution, $x=5$:<br />$-2\vert 8-5\vert -6=-12$<br />$-2\vert 3\vert -6=-12$<br />$-2(3)-6=-12$<br />$-6-6=-12$<br />$-12=-12$<br /><br />The equation is satisfied, so $x=5$ is a correct solution.<br /><br />Now let's substitute the second solution, $x=-11$:<br />$-2\vert 8-(-11)\vert -6=-12$<br />$-2\vert 8+11\vert -6=-12$<br />$-2\vert 19\vert -6=-12$<br />$-2(19)-6=-12$<br />$-38-6=-12$<br />$-44\neq-12$<br /><br />The equation is not satisfied, so $x=-11$ is not a correct solution.<br /><br />Therefore, Johan is not correct because there is only one solution: $x=5$.