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Q11.

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.$\mathbf{25}\mathbf{u}\mathbf{+}\mathbf{74}\mathbf{=}\mathbf{23}\mathbf{u}\mathbf{+}\mathbf{92}$

The solution for the equation $25u+74=23u+92$ is $u=9$.

See the step by step solution

## Step 1 – Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}25u+74=23u+92\\ 25u+74-74=23u+92-74\text{}\left(\text{subtract 74 from both sides}\right)\\ 25u=23u+1\text{}\left(\text{simplify}\right)\\ 25u-23u=23u-23u+18\text{}\left(\text{subtract 23u from both sides}\right)\\ 2u=18\text{}\left(\text{simplify}\right)\end{array}$

## Step 2 – Solve for u

Now, divide both sides of the equation by 2.

$\begin{array}{c}\frac{2u}{2}=\frac{18}{2}\\ u=9\end{array}$

Therefore, the solution of the equation is $u=9$.

## Step 3 – Check the solution

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

$25u+74=23u+92$

Now, substitute $u=9$ and check the result.

$\begin{array}{c}25×9+74=23×9+92\\ 225+74=207+92\\ 299=299\end{array}$

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