3/30 vert 2x+12vert lt 8 Which is the correct first step? 2x+12lt 8 and 2x+12 lt -8 2x+12lt 8 or 2x+12gt -8 2x+12lt 8 or 2x+12gt -8 2x+12lt 8 and 2x+12 gt -8

The correct first step is to split the absolute value inequality into two separate inequalities. The correct option is:<br /><br />$2x+12\lt 8$ or $2x+12\gt -8$<br /><br />Explanation:<br />The inequality $\vert 2x+12\vert \lt 8$ can be split into two separate inequalities:<br />1. $2x+12\lt 8$<br />2. $2x+12\gt -8$<br /><br />This is because the absolute value of a number is less than 8 if and only if the number is between -8 and 8. Therefore, the correct first step is to split the inequality into two separate inequalities.