Question 22103
First of all, the example shown by the teacher can only be correct if the 3x is negative.  Perhaps the equation was written down incorrectly, or the teacher made a mistake in her math, it happens sometime to everyone, even teachers.  the first answer you gave is the correct way to do this problem.  The only way I could get the teachers answer is if I changed the 3x to -3x.  Tell your child to be proud of themselves.  Everyone makes mistakes, that is how we learn, so either she/he copied the problem wrong, or the teacher made a mistake in her example.  See the importance of watching your signs?  the answer is totally different if you are not careful with neg and pos.

Ok, this is how I like to think about these problems. It works really well with teens.  Think of the equation as some sort of team event with the numbers being on one team and the variables (letters) being on the other team.  You must get each team member to the correct side of the = sign.  In the end every team must be on opposite sides. this can work for any problem with variables and numbers.
so let me work you problem
3x+8+7x=-62   
you must move the team members to the correct side of the = sign.  Remember anything you do to one side of the = sign, you must do to the other side to be fair.
I would do the following
3x+7x+8=-62  to get the 8 on its correct team subtract it from both sides. 
3x+7x+8-8=-62-8
3x+7x=-70    now you can add your x values together
10x=-70      but you still have a team member on the wrong side, the 10
             is multiplied by x, so to move it to the correct team you 
             must divide both sides by the number in front of the x.
10x/10=-70/10
x=-70/10     a neg. divided by a positive is still neg.
x=-7
Ok? I know this is a different answer than you gave in your example by the teacher. To get that answer, the 3x must be neg.  So there may be an issue with correctly writing the equation.  let me give you an example of my own.
7x+5-2x=20
7x-2x=20-5
5x=15
x=3
If you don't understand or have another problem, feel free to contact me at athompson022@ntcc.edu