You've done the right thing. In terms of a double inequality you can represent this as -17/5 < x < 3/5 given your calculations.
Hi, so |5x+7|<10 means that 5x+7<10 and -(5x+7)<10 right? And when I solved for x in both cases I get x<3/5 and x>-17/5 . Is this how you would solve a double inequality? Because I am not sure. Thank you in advance.