Students preferred dubstep, 25 % of the students liked trance music, and 20 % wanted to hear only house music. Fifteen percent of the respondents selected both dubstep and trance. The proportion of students that like either dubstep or trance is:

proportion of students that like either dubstep or trance is 40%

Step-by-step explanation:

Students preferring dubstep : Set [DS]  = 30%

Students preferring trance music : Set  [TM] = 25%

Students preferring house music : Set [HM] = 20%

Students preferring both dubstep & trance  : Set [DS ⋂ TM] = 15%

Formula : (A U B) = (A) + (B) - (A  ⋂ B)

[ DS U TM ] =  [DS] + [TM] - [DS ⋂ TM]

= 30% + 25%  - 15% → = 40%

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x