What negative value of x makes the equation 10+vert 3x+6vert =30 true? A -15(1)/(3) B -11(1)/(3) C -8(2)/(3) D -4(2)/(3)

To solve the equation $10+\vert 3x+6\vert =30$, we first isolate the absolute value expression by subtracting 10 from both sides of the equation:<br /><br />$\vert 3x+6\vert = 20$<br /><br />Next, we consider the two cases for the absolute value expression:<br /><br />Case 1: $3x+6 = 20$<br />$3x = 14$<br />$x = \frac{14}{3} = 4\frac{2}{3}$<br /><br />Case 2: $3x+6 = -20$<br />$3x = -26$<br />$x = -\frac{26}{3} = -8\frac{2}{3}$<br /><br />Therefore, the negative value of x that makes the equation true is $-8\frac{2}{3}$, which corresponds to option C.