Question

How do you solve $2.4\left( m-3 \right)+3.8=-8.2$?

Answer 1

Hint: We need to perform binary operations of addition and subtraction on the equation $2.4\left( m-3 \right)+3.8=-8.2$. It is a linear equation of m. we first complete the multiplication. Then we take all the constants together. We divide both sides of the equation with $2.4$ to get the final solution.

Complete step by step solution:
The given equation $2.4\left( m-3 \right)+3.8=-8.2$ is a linear equation of m. We need to simplify the equation by completing the multiplication of the constants separately.
All the terms in the equation of $2.4\left( m-3 \right)+3.8=-8.2$ are either variable of m or a constant. We break the multiplication by multiplying $2.4$ with $\left( m-3 \right)$.
So, $2.4\left( m-3 \right)=2.4m-7.2$.
The equation becomes $2.4m-7.2+3.8=-8.2$.
We take all the variables and the constants on one side and get $2.4m-7.2+3.8+8.2=0$.
There is only one variable which is $2.4m$.
Now we take the constants.
There are three such constants which are $-7.2,3.8,8.2$.
The binary operation between them is addition which gives us $-7.2+3.8+8.2=4.8$.
The final solution becomes
$\begin{align}
  & 2.4m-7.2+3.8+8.2=0 \\
 & \Rightarrow 2.4m+4.8=0 \\
\end{align}$.
Now we take the variable on one side and the constants on the other side.
\[\begin{align}
  & 2.4m+4.8=0 \\
 & \Rightarrow 2.4m=-4.8 \\
\end{align}\]
We divide both sides with $2.4$ to get
\[\begin{align}
  & \dfrac{2.4m}{2.4}=\dfrac{-4.8}{2.4} \\
 & \Rightarrow m=-2 \\
\end{align}\]
Therefore, the solution is $m=-2$.

Note: For the equation $2.4\left( m-3 \right)+3.8=-8.2$, we also could have left the multiplication for the end.
So, the equation gives $2.4\left( m-3 \right)=-8.2-3.8=-12$
We divide both sides with $2.4$ to get
\[\begin{align}
  & \dfrac{2.4\left( m-3 \right)}{2.4}=\dfrac{-12}{2.4} \\
 & \Rightarrow m-3=-5 \\
\end{align}\]
Now we add 3 to the both sides of the equation to get
$\begin{align}
  & m-3+3=-5+3 \\
 & \Rightarrow m=-2 \\
\end{align}$.