making a profit means ending the month with a number above 0, so your inequality will have to be greater than 0.
(sell) t-shirt = 12
(make) t-shirt = 6.50
and a constant of 150
so your current equation will be the cost of making a t-shirt, the money received by selling, and the cost of rent. it'll look like:
12t - 6.50t -150 > 0
but you want to get t alone to know how many t-shirts you have to sell, so solve the inequality:
12t - 6.50t - 150 > 0
12t - 6.50t > 150
5.50t > 150
t > (150/5.50)
and that fraction is roughly 27.27, so you'll round it up to the next whole number because alex can't make/sell a twenty-seventh of a t-shirt.
alex will have to make 28 t shirts to make a profit, and you can plug it back into the equality like so to check it:
12t - 6.50t - 150 > 0
12(28) - 6.50(28) - 150 > 0
336 - 182 - 150 > 0
4 > 0
and that statement is true, measly profit as it is.
