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Question
Solve the following equations for the unknown: `(6x + 7)/(3x + 2) = (4x + 5)/(2x + 3)`
Solution
`(6x + 7)/(3x + 2) = (4x + 5)/(2x + 3)`
⇒ (6x + 7)(2x + 3) = (4x + 5)(3x +2 )
⇒ 6x(2x + 3) + 7(2x + 3) = 4x(3x + 2) + 5(3x + 2)
⇒ 12x2 + 18x + 14x + 21 = 12x2 + 8x + 15x + 10
⇒ 18x + 14x + 21 = 8x + 15x + 10
⇒ 18x - 8x + 14x - 15x = 10 - 21
⇒ 9x = -11
⇒x = `-(11)/(9)`.
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