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Q11.

Expert-verified

Pre-algebra

Found in: Page 133

Book edition Common Core Edition

Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

Pages 183 pages

ISBN 9780547587776

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Short Answer

Solve the equation. Check your solution.
$25 u + 74 = 23 u + 92$

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1 – Separate the variable and constants

Write the original equation and separate the variable and constants.

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

Step 2 – Solve for u

Now, divide both sides of the equation by 2.

\begin{matrix} \frac{2 u}{2} = \frac{18}{2} \\ u = 9 \end{matrix}

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.

$25 u + 74 = 23 u + 92$

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

\begin{matrix} 25 \times 9 + 74 = 23 \times 9 + 92 \\ 225 + 74 = 207 + 92 \\ 299 = 299 \end{matrix}

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

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