Question

What is $4\left( 2m-n \right)-3\left( 2m-n \right)$ when m = -15 and n = -18?

Answer 1

Hint: Assume the given algebraic expression as E. Now, first of all simplify the given expression by taking $\left( 2m-n \right)$ common from both the terms and subtracting 3 from 4 inside the bracket formed. Once the expression is simplified substitute the given values of m and n in this expression and perform simple arithmetic operations required to get the answer.

Complete step by step solution:
Here we have been provided with the expression $4\left( 2m-n \right)-3\left( 2m-n \right)$ and we are asked to find its value at m = -15 and n = -18. First let us simplify the given expression.
Now, assuming the given expression as E we get,
$\Rightarrow E=4\left( 2m-n \right)-3\left( 2m-n \right)$
Here we can see that the binomial term $\left( 2m-n \right)$ is common in both the terms of the above expression, so taking this term common we get,
$\begin{align}
  & \Rightarrow E=\left( 2m-n \right)\left( 4-3 \right) \\
 & \Rightarrow E=\left( 2m-n \right)\times 1 \\
 & \Rightarrow E=\left( 2m-n \right) \\
\end{align}$
Substituting the given values of m = -15 and n = -18 in the above simplified expression we get,
$\begin{align}
  & \Rightarrow E=\left[ 2\left( -15 \right)-\left( -18 \right) \right] \\
 & \Rightarrow E=\left[ -30+18 \right] \\
 & \therefore E=-12 \\
\end{align}$
Hence, the value of the given expression is -12.

Note: Note that the main purpose of simplifying the given expression is to reduce the calculation. You can directly substitute the given values of m and n in the initial expression $4\left( 2m-n \right)-3\left( 2m-n \right)$. It is always better to search for the common terms in the algebraic expressions so that the calculation might get reduced. In case there are no other options then only we substitute the values without simplifying. You can also simplify the expression by separating the variables m and n by removing the brackets.