Question

Solve the equation. Check your solution.$\mathbf{2}\mathbf{m}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{5}(\mathbf{m}\mathbf{-}\mathbf{4})\mathbf{=}\mathbf{9}$

Short answer

The solution for the equation$2m+0.5(m-4)=9$ is$m=4.4$ .

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}2m+0.5(m-4)=9\\ 2m+0.5m-2=9\left[\text{distributiveproperty}\right]\\ \text{2.5}m-2=9\left[\text{combineliketerms}\right]\\ \text{2.5}m-2+2=9+2\left[\text{add2toeachside}\right]\\ \text{2.5}m=11\end{array}$

– Solve for m

Now, divide both sides of the equation by 2.5.

$\begin{array}{c}\text{2.5}m÷2.5=11÷2.5\\ m=4.4\end{array}$

Therefore, the solution of the equation is$m=4.4$ .

– Check the solution 

To check the solution, write the original equation and substitute the value ofm.

$2m+0.5(m-4)=9$

Now, substitute $m=4.4$and check the result.

$\begin{array}{c}2\times 4.4+0.5(4.4-4)=9\\ 8.8+0.5\times 0.4=9\\ 8.8+0.2=9\\ 9=9\end{array}$

As the left-hand side is equal to right hand side, this signifies that the solution is correct.