Question

If p is added to -5, the result is 7. Hence $3p=---$
A. $6$
B. $18$
C. $36$
D. $4$

Answer 1

Hint: In this problem we have given that If $p$ is added to $-5$, the result is $7$, hence we will add $p$ to $-5$ and equate it to $7$, then we will have the value of $p$. From the value of $p$ we will calculate the required value i.e. $3p$.

Complete step-by-step solution
Given that,
If $p$ is added to $-5$, the result is $7$. So mathematically we can write it as
$p+\left( -5 \right)=7$
We know that when we multiply a Positive integer/sign $\left( + \right)$ with the negative integer/sign we will get the negative integer/sign, i.e. $\left( + \right)\times \left( - \right)=\left( - \right)$. So when we multiply $-5$ with the Positive sign$\left( + \right)$ we will get $-5$. Then the above equation is modified as
$\begin{align}
  & p+\left( -5 \right)=7 \\
 & p-5=7 \\
\end{align}$
Adding $5$ on both sides of the above equation, then
$p-5+5=7+5....\left( \text{i} \right)$
In L.H.S we have something like $-a+a$. We know that when the same integer with different signs is added then we will get Zero value i.e. $-a+a=0$. So, the value of $-5+5$ is also $0$. When we add two positive integers then the sign of the result should be positive then $7+5=+12$.
Now substituting these values in equation$\left( \text{i} \right)$, then
$\begin{align}
  & p-5+5=7+5 \\
 & p+0=+12
\end{align}$
We can simply write it as $p=12$
Now the value of $3p$ is obtained by multiplying the value of $p$ with $3$, then
$\begin{align}
  & 3p=3\left( 12 \right) \\
 & =36
\end{align}$
Hence the value of $3p$ is $36$.

Note: We can also solve the above problem in another method. i.e. given that If $p$ is added to $-5$, the result is $7$, Mathematically
$\begin{align}
  & p+\left( -5 \right)=7 \\
 & p-5=7
\end{align}$
Multiplying $3$ on both sides of the above equation, then
$\begin{align}
  & 3\left( p-5 \right)=3\left( 7 \right) \\
 & 3p-15=21
\end{align}$
Adding $15$ on both the sides of the above equation, then
$\begin{align}
  & 3p-15+15=21+15 \\
 & 3p=36
\end{align}$
From both the methods we got the same answer.