b 3sqrt (x^2)+2x+1(voix lt 0)

To simplify the expression \(3\sqrt{x^2} + 2x + 1\) where \(x < 0\), follow these steps:<br /><br />1. Recognize that \(\sqrt{x^2} = |x|\).<br />2. Since \(x < 0\), \(|x| = -x\).<br /><br />Thus, \(\sqrt{x^2} = -x\).<br /><br />3. Substitute \(-x\) for \(\sqrt{x^2}\) in the expression:<br /><br />\[3\sqrt{x^2} + 2x + 1 = 3(-x) + 2x + 1\]<br /><br />4. Simplify the expression:<br /><br />\[3(-x) + 2x + 1 = -3x + 2x + 1\]<br /><br />5. Combine like terms:<br /><br />\[-3x + 2x + 1 = -x + 1\]<br /><br />Therefore, the simplified expression is:<br /><br />\[-x + 1\]