Question

Solve the following equation by trial and error method: $\text{5p}+\text{2}=\text{17}$.

Answer 1

Hint: In this question, we are given an equation in terms of variable p and we have to solve it which means we need to find the value of p. We have to solve it using trial and error methods. For this, we will try to put different values of p one by one in the equation and check if the left hand side is equal to the right hand side of the equation. We will start from p = 0 and proceed till we find our required value which satisfies the equation.

Complete step by step answer:
Here, we are given the equation as \[\text{5p}+\text{2}=\text{17}\cdots \cdots \cdots \cdots \left( 1 \right)\]
We need to find the value of p using trial and error methods. For this, we will put different values of p to check if the left hand side of the equation becomes equal to the right hand side of the equation.
Let us put the value of p as 0 in equation (1) we get:
\[\begin{align}
  & \text{5}\left( 0 \right)+\text{2}=\text{17} \\
 & \Rightarrow \text{0+2=17} \\
 & \Rightarrow \text{2=17} \\
\end{align}\]
But this is not true. So, p cannot be equal to 0. So let us now put value of p as 1 in equation (1) we get:
\[\begin{align}
  & \text{5}\left( 1 \right)+\text{2}=\text{17} \\
 & \Rightarrow \text{5+2=17} \\
 & \Rightarrow \text{7=17} \\
\end{align}\]
But this is not true. So, p cannot be equal to 1. So let us now put value of p as -1 in equation (1) we get:
\[\begin{align}
  & \text{5}\left( -1 \right)+\text{2}=\text{17} \\
 & \Rightarrow -\text{5+2=17} \\
 & \Rightarrow -\text{3=17} \\
\end{align}\]
But this is not true. So, the value of p cannot be equal to -1. Now let us put value of p as 2 in equation (1) we get:
\[\begin{align}
  & \text{5}\left( 2 \right)+\text{2}=\text{17} \\
 & \Rightarrow 1\text{0+2=17} \\
 & \Rightarrow 1\text{2=17} \\
\end{align}\]
But this is not true. So, the value of p cannot be equal to 2. Now let us put value of p as -2 in equation (1), we get:
\[\begin{align}
  & \text{5}\left( -2 \right)+\text{2}=\text{17} \\
 & \Rightarrow -1\text{0+2=17} \\
 & \Rightarrow -8\text{=17} \\
\end{align}\]
But this is not true. So the value of p cannot be equal to -2. Now let us put value of p as 3 in equation (1) we get:
\[\begin{align}
  & \text{5}\left( 3 \right)+\text{2}=\text{17} \\
 & \Rightarrow 15\text{+2=17} \\
 & \Rightarrow 17\text{=17} \\
\end{align}\]
This is true. Therefore, the value of p as 3 satisfies the equation (1).

So, p = 3 is our required answer.

Note: Students should note that we have used trial and error methods for solving this equation only because it was given, otherwise this method is not reliable. This method requires a lot of trials and sometimes values are large and we cannot guess them. Students should take care of signs while solving the equations. Do not forget to consider negative values too as they can be the answer too.