Question

1. A checking account is set up with an initial balance of $4800, and $400 is removed from the account each month for rent (no other transactions occur on the account). Write and solve an inequality to find m, the number of months the account balance remains above $2000.

Answer 1

The given situation can be written algebricaly as follow:

4800 - 400m > 2000

4800 is the initial value of the check acount, for the month m, the value of the account is decreased in 400m, and it is necessary that the money remains above 2000.

Solve the previous inequality for m, just as follow:

4800 - 400m > 2000 subtract 4800 both sides

-400m > 2000 - 4800

-400m > -2800 divide by -400 both sides

m < (-2800)/(-400) the sense of the inequality change by the division by -

m < 7

Hence, the account balance remains above 2000 for a time lower than 7 months