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Expert-verified Found in: Page 127 ### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776 # Solve the equation. Check your solution.$\mathbf{2}\mathbf{m}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{5}\left(\mathbf{m}\mathbf{-}\mathbf{4}\right)\mathbf{=}\mathbf{9}$

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

See the step by step solution

## Step 1 – Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}2m+0.5\left(m-4\right)=9\\ 2m+0.5m-2=9\text{}\left[\text{distributive property}\right]\\ \text{2.5}m-2=9\text{}\left[\text{combine like terms}\right]\\ \text{2.5}m-2+2=9+2\text{}\left[\text{add 2 to each side}\right]\\ \text{2.5}m=11\text{}\end{array}$

## Step 2 – 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$m=4.4$ .

## Step 3 – Check the solution

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

$2m+0.5\left(m-4\right)=9$

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

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

As the left-hand side is equal to right hand side, this signifies that the solution is correct. ### Want to see more solutions like these? 