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