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

Explanation

`(2x-3)/(3x+2)=-2/3`
Let us perform cross-multiplication we get,
`=> 3(2x – 3) = -2(3x + 2) `
`=>6x – 9 = -6x – 4 `
When rearranged,
`=> 6x + 6x = 9 – 4 `
`=>12x = 5`
`=> x = 5/12`
Now let us verify the given equation,
`(2x-3) / (3x+2) = -2/3 `
By substituting the value of `x` we get,
`=>(2(5/12) – 3) / (3(5/12) + 2) = -2/3`
`=> ((5/6)-3) / ((5/4) + 2) = -2/3`
`=>((5-18)/6) / ((5+8)/4) = -2/3`
`=>(-13/6) / (13/4) = -2/3 `
`=>(-13/6) xx (4/13) = -2/3 `
`=>-4/6 = -2/3 `
`=>-2/3 = -2/3`
Hence, the given equation is verified.