Question

4/3 (2x/3 + 1/2) = x/6 - 5/3

Answer 1

The value of x is
`-(42)/(13)`

Explanation:

The expression is
`(4)/(3) ((2x)/(3) +(1)/(2) )=(x)/(6) -(5)/(3)`

To find the value of x, we need to simplify the equation,

Multiply the term
`((2x)/(3) +(1)/(2) )` by
`(4)/(3)`,

`(8x)/(9) +(4)/(6) =(x)/(6)-(5)/(3)`

Subtracting by
`(x)/(6)` and
`(4)/(6)` on both sides of the equation, we get,

`(8x)/(9) -(x)/(6) =-(5)/(3)-(4)/(6)`

Taking LCM on both sides,

`(48x-9x)/(54) =(-10-4)/(6)`

Simplifying, we get,

`(39x)/(54) =-(14)/(6)`

Multiplying both sides by 54,

`39x=(-14(54))/(6) \\39x=-14(9)\\39x=-126`

Dividing both sides by 39, we get,

`x=-(42)/(13)`

Thus, the value of x is
`-(42)/(13)`