(x−6) First, let's remove the fractions by multiplying both sides by 6 (the least common multiple of 2 and 3 ): 6⋅‌
1
2
(‌
3x
5
+4)≥6⋅‌
1
3
(x−6)
This simplifies to: 3(‌
3x
5
+4)≥2(x−6) Next, distribute the 3 and the 2 inside the parentheses: 3⋅‌
3x
5
+3⋅4≥2⋅x−2⋅6 Which further simplifies to: ‌
9x
5
+12≥2x−12 To clear the fraction, multiply everything by 5 :
5⋅‌
9x
5
+5⋅12≥5⋅2x−5⋅12 This simplifies to: 9x+60≥10x−60 Subtract 9 x from both sides: 60≥x−60 Then add 60 to both sides:
120≥x This can be written as: x≤120 In interval notation, this is expressed as: x∈(−∞,120] Therefore, the correct option is: Option B: x∈(−∞,120]