Simplify (write without the absolute value sign) |x-120| if x <120

This is so hard and it’s for a test

Acaterer charges $500 plus $30 per guest to cater a wedding. walt and traci don't want to spend more than $8000 on catering. write and solve an inequality in terms of the number of guests, g, that can be invited. a) 30g ? 8000; g ? 267 b) 500g < 8000; g < 16 c) 500 + 30g < 8000; g < 250 d) 500 + 30g ? 8000; g ? 250

What would be the reasons for lines 3 and 4? a. addition property; subtraction property b. addition property; solve c. substitution property; subtraction property d. substitution property; prove