Question 200909
{{{5/7<=x-5/3<2}}} Start with the given compound inequality.



{{{cross(21)^3(5/cross(7))<=21x-cross(21)^7(5/cross(3))<21*2}}} Multiply EVERY term by the LCD {{{21}}} to clear out any fractions.



{{{3(5)<=21x-7(5)<21*2}}} Simplify



{{{15<=21x-35<42}}} Multiply



{{{15+35<=21x<42+35}}} Add {{{35}}} to all sides.



{{{50<=21x<42+35}}} Combine like terms on the left side.



{{{50<=21x<77}}} Combine like terms on the right side.



{{{(50)/21<=x<(77)/21}}} Divide all sides by 21.



{{{50/21<=x<11/3}}} Reduce.



So the solution is {{{50/21<=x<11/3}}}