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Q22.

Expert-verified
Found in: Page 133

### 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.$\mathbf{2}\left(\mathbf{-}\mathbf{4}\mathbf{h}\mathbf{-}\mathbf{13}\right)\mathbf{=}\mathbf{37}\mathbf{+}\mathbf{13}\mathbf{h}$

The solution for the equation $2\left(-4h-13\right)=37+13h$ is $h=-3$.

See the step by step solution

## Step 1 – Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}2\left(-4h-13\right)=37+13h\\ -8h-26=37+13h\\ -8h-13h-26=37+13h-13h\text{}\left(\text{Subtract}13h\text{from both sides}\right)\\ -21h-26=37\\ -21h-26-37=37-37\text{}\left(\text{Subtract 37 from both sides}\right)\\ -21h-63=0\\ -21h=63\end{array}$

## Step 2 – Solve for h

Now, divide both sides of the equation by -21.

$\begin{array}{c}\frac{-21h}{-21}=\frac{63}{-21}\\ h=-3\end{array}$

Therefore, the solution of the equation is $h=-3$.

## Step 3 – Check the solution

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

$2\left(-4h-13\right)=37+13h$

Now, substitute $h=-3$ and check the result.

$\begin{array}{c}2\left(-4\left(-3\right)-13\right)=37+13\left(-3\right)\\ 2\left(12-13\right)=37-39\\ 2\left(-1\right)=-2\\ -2=-2\end{array}$

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

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