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Question
Solve the following:
`1/2(x + 1) + 1/3(x - 1) = 5/12(x - 2)`
Solution
Given, `1/2(x + 1) + 1/3(x - 1) = 5/12(x - 2)`
⇒ `x/2 + 1/2 + x/3 - 1/3 = (5x)/12 - 5/6`
⇒ `x/2 + x/3 - (5x)/12 = 1/3 - 1/2 - 5/8` ...[Transposing `1/2, 1/3` to RHS and `(5x)/12` to LHS]
⇒ `(6x + 4x - 5x)/12 = (2 - 3 - 5)/6`
⇒ `(5x)/12 = (-6)/6`
⇒ `5x xx 6 = (-6) xx 12` ...[By cross-multiplication]
⇒ `x = ((-6) xx 12)/(5 xx 6)`
∴ `x = (-12)/5`
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