Write and solve an inequality for x.

C

Step-by-step explanation:

Using the Triangle Inequality Theorem, the sum of two sides must be greater than the third side.

BD + DC > BC     and        DC + BC > BD      and          BD + BC >   DC

x+3 + DC > 9       and         DC + 9 > x+3       and          x+3 + 9 > DC

                                                   -3       -3  

                                            DC + 6 > x

                                             x < DC + 6

If x + 3 + DC > 9, then obviously x + 3 > 9

Similarly, if x < DC + 6, then obviously x < 6