Two different points on a number line are both 3 units from the point with coordinate -4 . The solution to which of the following equations gives the coordinates of both points? A) vert x+4vert =3 B) vert x-4vert =3 C) vert x+3vert =4 D) vert x-3vert =4 A B C D

To find the coordinates of the two points that are 3 units away from the point with coordinate -4, we can use the absolute value equation.<br /><br />The absolute value of a number represents its distance from zero on the number line. Therefore, the absolute value of the difference between a point and -4 will give us the distance between that point and -4.<br /><br />Let's analyze each option:<br /><br />A) $\vert x+4\vert =3$<br />This equation represents the distance between a point and -4 being equal to 3 units. Solving this equation, we get:<br />$x+4=3$ or $x+4=-3$<br />Solving for x, we get:<br />$x=-1$ or $x=-7$<br />So, the coordinates of the two points are -1 and -7.<br /><br />B) $\vert x-4\vert =3$<br />This equation does not represent the distance between a point and -4 being equal to 3 units. It represents the distance between a point and 4 being equal to 3 units.<br /><br />C) $\vert x+3\vert =4$<br />This equation does not represent the distance between a point and -4 being equal to 3 units. It represents the distance between a point and -3 being equal to 4 units.<br /><br />D) $\vert x-3\vert =4$<br />This equation does not represent the distance between a point and -4 being equal to 3 units. It represents the distance between a point and 3 being equal to 4 units.<br /><br />Therefore, the correct answer is A) $\vert x+4\vert =3$.