Question 1123449
your equation is y = 2570 - 125.5 * x


you want to know when 1600 < y < 2000


since y = 2570 - 125.5 * x, then you can replace y with 2570 - 125.5 * x and you then want to know when 1600 < 2570 - 125.5 * x < 2000


subtract 2570 from all sides of this inequality to get:


1600 - 2570 < -125.5 * x < 2570 - 2000


multiply all sides of this inequality by -1 to get:


-(1600 - 2570 > 125.5 * x > -(2570 - 2000)


simplify to get 970 > 125.5 * x > 570


divide all sides of this inequality by 125.5 to get 970 / 125.5 > x > 570 / 125.5


simplify to get 7.729083665 > x > 4.541832669


your answer will be somewhere between 4 and 8.


when x = 4, y = 2570 - 125.5 * x = 2068
when x = 5, y = 2570 - 125.5 * x = 1942.5 which is < 2000


when x = 8, y = 2570 - 125.5 * x = 1566
when x = 7, y = 2570 - 125.5 * x = 1691.5 which is > 1600


your answer is that 1600 < y < 2000 when x = 5 to 7.


you could have analyzed this from the answer of  7.729083665 > x > 4.541832669


if x > 4.541832669, then x > 4 which means x >= 5.


if x < 7.729083665, then x < 8 which means x <= 7.


x >= 5 and x <= 7 gets you x = 5 or 6 or 7, as long as x has to be an integer.


if you're in doubt, then doing it the way i did it above by checking x = 7,8,4,5 is a good way to be sure you got it right.