Question

If y =
$\frac{x + 1}{2}$
find the value of x from the equation 2y - 3 = 3(y+1) - 8

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Answer 1

$\text{It is given that }$

$y = \dfrac{x+1}{2} \text{ ------ (i)}$

$2y-3 = 3(y+1) - 8 \text{ ------ (ii)}$

$\text{Upon simplifying (ii) we get}$

$\implies 2y - 3 = 3y + 3 - 8$

$\implies 2y - 3 = 3y - 5$

$\implies 2y - 3y = -5 + 3$

$\implies -y = -2$

$\implies y = 2$

$\text{Substituting the value from (i)}$

$\implies \dfrac{x+1}{2} = 2$

$\implies x+1 = 4$

$\implies \boxed{x = 3}$