Question

If $\frac{1}{2}p+1=\frac{3}{2}p+2$, then the value of $p$ is

• A. $1$
• B. $-1$
• C. $\frac{1}{2}$
• D. $-\frac{1}{2}$

Answer 1

The correct option is B

$-1$

Explanation for the correct answer

Option B

$\frac{1}{2}p+1=\frac{3}{2}p+2$ ( given )

$\frac{1}{2}p-\frac{3}{2}p=2-1$ ( Transposing the like terms to one side of equation )

$p\left[\frac{1}{2}-\frac{3}{2}\right]=1$

$p\left[\frac{1-3}{2}\right]=1$ ( Solving rational numbers on L.H.S )

$p\left[\frac{-2}{2}\right]=1$ ( solving the numerator )

$p\times (-1)=1$

$\frac{-p}{-1}=\frac{1}{-1}$ ( Dividing both sides by $-1$)

[ NOTE : Alternatively, we can find the value of $p$ by substituting the values given in options one by one and checking which value will satisfy or give same value of L.H.S and R.H.S. The value which will satisfy both L.H.S and R.H.S will be the value of $p$.]

Therefore, the value of $p=-1$.

Hence, Option B is correct answer.