Clara is growing her hair out and wants it to be no longer than 15 cm but more than 11 cm. her hair is 7 cm right now and grows at a rate of 0.25 cm per week. the compound inequality 11 < 7 + 0.25t ≤ 15 models the scenario. how long will it take clara to grow out her hair to the desired length?

For this case we have the following compound inequality:
 11 <7 + 0.25t ≤ 15
 We must solve this inequality for time.
 We have then:

 For 11 <7 + 0.25t:
 11 <7 + 0.25t
 11 - 7 <0.25t
 4 <0.25t
 4 / 0.25 <t
 16 <t

For 7 + 0.25t ≤ 15:
 7 + 0.25t ≤ 15
 0.25t ≤ 15 - 7
 0.25t ≤ 8
 t ≤ 8 / 0.25
 t ≤ 32

 Therefore, the answer is:
 16 <t ≤ 32

 
 16 <t ≤ 32
 Clara has the desired length in more than 16 weeks, but up to 32 weeks.