Question

How do you solve $-10p+9p=12$?

Answer 1

Hint: The given equation $-10p+9p=12$ is a linear equation in the variable $p$, since the highest power of $p$ is equal to one. Therefore, it will have a single solution. For solving it, we will use the associative property of multiplication, which is $ab+ac=a\left( b+c \right)$ to simplify the LHS of the given equation to take the variable $p$ common. Then on solving the expression inside the bracket, the given equation will become simplified. Finally, on multiplying both sides of the simplified equation by $-1$, we will get the final solution.

Complete step by step solution:
The equation given to us is written as
$\Rightarrow -10p+9p=12$
Solving this equation means finding the value of the variable $p$ which on substituting in the given equation will satisfy it. Now, for solving the above equation, we have to simplify the LHS. For that, we use the associative property of the algebraic multiplication, which is given by $ab+ac=a\left( b+c \right)$ to write the LHS of the above equation as
$\begin{align}
  & \Rightarrow p\left( -10+9 \right)=12 \\
 & \Rightarrow p\left( -1 \right)=12 \\
 & \Rightarrow -p=12 \\
\end{align}$
Finally, on multiplying the both sides of the above equation by $-1$ we get
\[\begin{align}
  & \Rightarrow \left( -p \right)\times \left( -1 \right)=12\times \left( -1 \right) \\
 & \Rightarrow p=-12 \\
\end{align}\]

Hence, we got the solution of the given equation as $p=-12$.

Note: Do not forget to multiply the equation $-p=12$ by $-1$, as done in the last step. This is because the variable in the given equation is $p$ not $-p$ and so we have to determine the value of $p$ not that of $-p$. Also, for checking for the calculation mistakes that might occur in your solution, always back substitute the final solution into the given equation and check whether the LHS is coming equal to the RHS or not.