solve for x and write answer in interval notation

Question

solve for x and write answer in interval notation 3x/x-2 ≤ 0

Answer 1

3x/x-2 ≤ 0

 

(Multiply both sides by "x-2")

 

3x²-6x ≤ 0

 

Use quadratic formula to solve

 

a=3, b=-6, c=0

 

x = [-b ± √(b² - 4ac)] / 2a

 

   = 6 ± √(36 - 4(3)(0)] / 6

 

   = 6 ± √(36 - 0) / 6

 

   = 6 ± √(36) / 6

 

   = 6 ± 6 / 6

 

   = (6 + 6) / 6 = 12/6 = 2

   = (6 - 6) / 6 = 0/6 = 0

 

Answer: 0 ≤ x < 2 (the last symbol IS a less-than and not a less-than-or-equal-to sign, since, when x=2, the value of the original expression = 0/0, which is indeterminate)