vert x-3vert +2=4 -1,5 (9) 1,5 -5 Multiple Choice 1 point

To solve the equation \(\vert x-3\vert +2=4\), we first isolate the absolute value expression:<br /><br />\[<br />\vert x-3\vert + 2 = 4<br />\]<br /><br />Subtract 2 from both sides:<br /><br />\[<br />\vert x-3\vert = 2<br />\]<br /><br />The absolute value equation \(\vert x-3\vert = 2\) means that \(x-3\) can be either 2 or -2. Therefore, we have two cases to consider:<br /><br />1. \(x-3 = 2\)<br />2. \(x-3 = -2\)<br /><br />Solving these equations:<br /><br />1. \(x-3 = 2\)<br /> \[<br /> x = 5<br /> \]<br /><br />2. \(x-3 = -2\)<br /> \[<br /> x = 1<br /> \]<br /><br />So the solutions to the equation are \(x = 1\) and \(x = 5\).<br /><br />Therefore, the correct answer is:<br />\[<br />\{1, 5\}<br />\]