How do you solve 8x+9<9x- 8 or x-6>2x-7?

Inequalities can be treated just like equations with one major difference - if you multiply or divide both sides using a negative number then  the Inequality Sign is reversed. This doesn't actually apply in these questions.

1) 8x + 9 < 9x -  8...add 8 to both sides and subtract 8x from both sides
17 < x...it's normal practise to put x as the subject.
X > 17

2) x - 6 > 2x - 7...add 7 to both sides and subtract x from both sides
1 > x...and putting x as the subject
x < 1

You can't solve either of them because it has a multiplication sign and a division sign next to each other which doesn't work.