Question

How do you solve $p = 2p + 3$ ?

Answer 1

Hint:Here, we are given the linear equation with one variable. To solve this equation, we will first bring the terms with the variable to the left side and other terms to the right side. After that, we need to use the concept of multiplication or division in simple equations.

Complete step by step answer:
We are given $p = 2p + 3$.Here, we have two terms with variables on both sides. Therefore, we will first bring them together on the left hand side and move the constant term to the right hand side.
\[p - 2p = 3 \\
\Rightarrow - p = 3\]
Now, to find the variable $p$, we need to remove the digit $ - 1$ which is multiplied with it. This can be done by dividing the right hand side by $ - 1$. However, it is important to know that we need to perform any arithmetic operation on both the sides of the equation.
Therefore, we will divide both the sides of the equation by $ - 1$.
\[ \Rightarrow \dfrac{{ - p}}{{ - 1}} = \dfrac{3}{{ - 1}}\]
Now, we know that when there is the same number in the numerator and the denominator, it gets cancelled out. Therefore, here, we can cancel out the digit $ - 1$ or the minus sign on the left hand side of the equation which will give us:
$ \therefore p = - 3$
Thus our final answer is $ - 3$.

Note:It is important to keep in mind that while solving a simple equation, we need to think of the equation as a balance. Thus, if we do something to one side of the equation, we must do the same thing to the other side. Doing the same thing to both sides of the equation keeps the equation balanced. For example, we have divided both the sides by $ - 1$ in this problem.