Question

How do you simplify $4p+9+\left( -7p \right)+2$?

Answer 1

Hint: This is an expression which is a combination of variables and constants. It is not an equation as it is not equated to anything. So it is just an expression. And to simplify these kinds of questions, all we need to make use of is simple and basic mathematics. We just have to group variables of one kind to one side and constants to the other side so as to perform the necessary manipulations. And then add or subtract as per the question to get the answer.

Complete step by step solution:
The expression in the question is $4p+9+\left( -7p \right)+2$.The variable in the question is $p$.
So now let us group the variables together.
Upon doing so, we get the following :
$\begin{align}
  & \Rightarrow 4p+9+\left( -7p \right)+2 \\
 & \Rightarrow 4p-7p+9+2 \\
\end{align}$
Upon grouping the variables, the constants are itself grouped.
So now let us add the variables.
Upon doing so, we get the following :
$\begin{align}
  & \Rightarrow 4p+9+\left( -7p \right)+2 \\
 & \Rightarrow 4p-7p+9+2 \\
 & \Rightarrow -3p+9+2 \\
\end{align}$
Now let us add the constants.
Upon doing so, we get the following :
$\begin{align}
  & \Rightarrow 4p+9+\left( -7p \right)+2 \\
 & \Rightarrow 4p-7p+9+2 \\
 & \Rightarrow -3p+9+2 \\
 & \Rightarrow -3p+11 \\
\end{align}$

$\therefore $ Hence, upon solving $4p+9+\left( -7p \right)+2$, we get the result $-3p+11$.

Note: We would have solved for the value of $p$ if the expression is equated to some value. Since, it is not equated to anything, we just have to leave the answer as it is. We should be careful while manipulating the terms in the expression. We should be careful while adding or subtracting , or else it would lead to calculation errors and the result and the entire process would go wrong.