Answer:
[tex]\large\boxed{x\leq\dfrac{39}{25}}[/tex]
Step-by-step explanation:
[tex]1-\dfrac{1}{3}x\geq\dfrac{1}{2}\left(x-\dfrac{3}{5}\right)\qquad\text{use distributive property}\ a(b+c)=ab+ac\\\\1-\dfrac{1}{3}x\geq\dfrac{1}{2}x-\dfrac{3}{10}\qquad\text{multiply both sides by}\ LCM(3,\ 2,\ 10)=30\\\\(30)(1)-(30)\left(\dfrac{1}{3}x\right)\geq(30)\left(\dfrac{1}{2}x\right)-(30)\left(\dfrac{3}{10}\right)\\\\30-10x\geq15x-(3)(3)\\\\30-10x\geq15x-9\qquad\text{subtract 30 from both sides}\\\\-10x\geq15x-39\qquad\text{subtract 15x from both sides}\\\\-25x\geq-39\qquad\text{change the signs}\\\\25x\leq39\qquad\text{divide both sides by 25}\\\\x\leq\dfrac{39}{25}[/tex]
