Question

Which of the following is the solution to the inequality below? 1-1/3x>=1/2(x-3/5)

Answer 1

`\large\boxed{x\leq(39)/(25)}`

Explanation:

`1-(1)/(3)x\geq(1)/(2)\left(x-(3)/(5)\right)\qquad\text{use distributive property}\ a(b+c)=ab+ac\\\\1-(1)/(3)x\geq(1)/(2)x-(3)/(10)\qquad\text{multiply both sides by}\ LCM(3,\ 2,\ 10)=30\\\\(30)(1)-(30)\left((1)/(3)x\right)\geq(30)\left((1)/(2)x\right)-(30)\left((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(39)/(25)`