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Question
Solve the following equation:
`("2x" - 13)/5 - ("x" - 3)/11 = ("x" - 9)/5 + 1`
Solution
`("2x" - 13)/5 - ("x" - 3)/11 = ("x" - 9)/5 + 1/1`
Since, L.C.M. of denominators 5, 11, 5 and 1 = 55
`therefore ("2x" - 13)/5 xx 55 - ("x" - 3)/11 xx 55 = ("x" - 9)/5 xx 55 + 1/1 xx 55`
⇒ 11(2x - 13)-5 (x - 3) = 11(x - 9) + 55
⇒ 22x - 143 - 5x + 15 = 11x - 99 + 55
⇒ 22x - 5x - 11x = -99 + 55 + 143 - 15
⇒ 6x = 198 - 114
⇒ 6x = 84
⇒ x = `84/6`
⇒ x = 14
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