Multiple Choice 1 point vert x+5vert -3=7 0,-15 (infty ,9)cap (5,infty ) 5,-15 9,5

To solve the equation $\vert x+5\vert -3=7$, we first isolate the absolute value expression by adding 3 to both sides of the equation:<br /><br />$\vert x+5\vert -3+3=7+3$<br /><br />$\vert x+5\vert =10$<br /><br />The absolute value of a number is the distance of that number from zero on the number line. Therefore, the equation $\vert x+5\vert =10$ means that the distance of $x+5$ from zero is 10. This can happen in two cases:<br /><br />Case 1: $x+5=10$<br />In this case, we subtract 5 from both sides of the equation to solve for $x$:<br /><br />$x+5-5=10-5$<br /><br />$x=5$<br /><br />Case 2: $x+5=-10$<br />In this case, we subtract 5 from both sides of the equation to solve for $x$:<br /><br />$x+5-5=-10-5$<br /><br />$x=-15$<br /><br />Therefore, the solution set for the equation $\vert x+5\vert -3=7$ is $\{5,-15\}$.<br /><br />The correct answer is $\{5,-15\}$.