Question

Solve: 5x - 2(2x - 7) = 2(3x - 1) + `7/2`

Answer 1

Let us open the brackets,

`"LHS" = 5x - 4x + 14 = x + 14`.

`"RHS" = 6x - 2 + 7/2 = 6x - 4/2 + 7/2 = 6x + 3/2`.

The equation is `x + 14 = 6x + 3/2`

or  `14 = 6x - x + 3/2`

or  `14 = 5x + 3/2`

or  `14 - 3/2 = 5x`

or  `(28 - 3)/2 = 5x`

or  `25/2 = 5x`

or `x = 25/2 xx 1/5 = (5 xx 5)/(2 xx 5) = 5/2`.

Therefore, required solution is `x = 5/2`

Check:

`"LHS" = 5 xx 5/2 - 2(5/2 xx 2 - 7) = 25/2 - 2(5 - 7) = 25/2 - 2(- 2) = 25/2 + 4 = (25 +8)/2 = 33/2.`

`"RHS" = 2(5/2 xx 3 - 1) + 7/2 = 2(15/2 - 2/2) + 7/2 = (2 xx 13)/2 + 7/2 = (26 + 7)/2 = 33/2.`

LHS = RHS.    ....(As required)