Solve the equation and verify your answer: `(2x+1)/(3x-2)=5/9`

Explanation

`(2x+1)/(3x-2)=5/9`
Do the cross multiplication,
We get,
`=>9 ( 2x + 1 ) = 5 ( 3x -2 )`
`=>18x + 9 = 15x - 10`
`=>18x - 15x = -10 - 9`
`=>3x = -19`
`=>x = - 19 / 3`

Verification:
By substituting the value of `x` we get,
`=>(2(-19/3) + 1) / (3(-19/3) – 2) = 5/9 `
`=>(-38/3 + 1) / (-57/3 – 2) = 5/9 `
`=>(-38 + 3)/3 / (-57 – 6)/3 = 5/9`
`=> -35/3 / -63/3 = 5/9`
`=> -35/3 × 3/-63 = 5/9`
`=> -35/-63 = 5/9`
`=>5/9 = 5/9`
Hence, the given equation is verified.