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Q30.

Expert-verifiedFound in: Page 127

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.$\mathbf{2}\mathbf{m}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{5}(\mathbf{m}\mathbf{-}\mathbf{4})\mathbf{=}\mathbf{9}$**

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

Write the original equation and separate the variable and constants.

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

Now, divide both sides of the equation by 2.5.

$\begin{array}{c}\text{2.5}m\xf72.5=11\xf72.5\\ m=4.4\end{array}$

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

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

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

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.

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