Linear Inequality word problem

Question

When the temperature in the clouds is 7 deg F plus or minus 3 deg F, star-shaped crystals form. At 14 deg F plus or minnus 4 deg F, plate-shaped crystals are formed.

a) Find the range of temperature that produces star-shaped crystals

b)Find the range of temperature that produces plate-shaped crystals

Answer 1

a). To answer this question, we'll let t_s represent the temperature at which star-shaped crystals form. Since we are looking for a range of temperatures and not just specific temperatures, we know that we need to use an inequality. t_s has to be between (7-3)°F and (7+3)°F, so we can write (7-3)<t_s<(7+3), or 4<t_s<10. In other words, the range of temperatures that produce star-shaped crystals is 4°F to 10°F. 

b.) Let t_p represent the temperature at which plate-shaped crystals form. t_p has to be between (14-4)°F and (14+4)°F, so we can write (14-4)<t_p<(14+4), or 10<t_p<18. In other words, the range of temperatures that produce plate-shaped crystals is 10°F to 18°F.