If 1 2 ( 3 x 5 +4 ) 1 3 (x-6), x R then

Step-by-step solution

Given the inequality 1 2 ( 3x 5 + 4 ) 1 3 (x - 6) . Multiplying both sides by 6 to clear the denominators: 3 ( 3x 5 + 4 ) 2(x - 6) Expanding both sides: 9x 5 + 12 2x - 12 Rearranging the terms to isolate x : 12 + 12 2x - 9x 5 24 10x - 9x 5 24 x 5 Multiplying by 5 : 120 x or x 120 . Thus, the solution set is x (- , 120] . Answer: x (- , 120]