Alex sells t-shirts. it costs alex $6.50 to buy each t-shirt. alex also pays $150 each month to rent equipment to add print to the t-shirts. alex sells each t-shirt for $12. write an inequality that can be used to determine the number of t-shirts (t) alex must sell each month in order to make a profit for the month.

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.