Question

Solve for x:
1 1/5x−2 1/3<1/7x+1 1/2

Answer 1

Answer:
`x<3(175)/(222)`

Explanation:

`1(1)/(5)x-2(1)/(3)<(1)/(7)x+1(1)/(2)`

Add
`2(1)/(3)` on both sides and subtract
`(1)/(7)x` on both sides to leave x's on the left side and independent values on the right.

`(2(1)/(3)-(1)/(7)x) +1(1)/(5)x-2(1)/(3)<(1)/(7)x+1(1)/(2)+(2(1)/(3)-(1)/(7)x)`

`1(1)/(5)x-(1)/(7)x<1(1)/(2)+2(1)/(3)`

Solve the fractions.

`1((1)/(5)-(1)/(7))x<1+2((1)/(2)+(1)/(3))`

`1(((1)(7)-(5)(1))/((5)(7)) )x<3(((1)(3)+(2)(1))/((2)(3)) )`

`1((7-5)/(35) )x<3((3+2)/(6) )`

`1((2)/(35) )x<3((5)/(6))`

`1(2)/(35)x<3(5)/(6)`

Convert the mixed fraction
`1(2)/(35)` to an improper fraction. You can do this by multiplying 1 times 35 and adding 2.

`(37)/(35)x<3(5)/(6)`

Now use the reciprocal (inverse fraction) and multiply on both sides to isolate x.

`((35)/(37)) ((37)/(35))x <(3(5)/(6))((35)/(37))`

`x<3((5)/(6)*(35)/(37))`

`x<3((175)/(222) )`

`x<3(175)/(222)`