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Q3.

Expert-verified

Pre-algebra

Found in: Page 126

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. $13 = 2 y - 3 (y + 4)$

The solution for the equation $13 = 2 y - 3 (y + 4)$ is localid="1650416876257" $y = - 25$ .

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.

$\begin{matrix} 13 + 12 = 2 y - 3 y - 12 + 12 \\ 25 = 2 y - 3 y \\ - y = 25 \end{matrix}$

Step 2 – Solve for y

Now, multiply both sides of the equation by -1.

$\begin{matrix} - y (- 1) = 25 (- 1) \\ y = - 25 \end{matrix}$

Therefore, the solution of the equation is $y = - 25$ .

Step 3 – Check the solution

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

$13 = 2 y - 3 (y + 4)$

Now, substitute $y = 25$ and check the result.

$\begin{matrix} 13 = 2 (- 25) - 3 ((- 25) + 4) \\ 13 = - 50 - 3 (- 21) \\ 13 = - 50 + 63 \\ 13 = 13 \end{matrix}$

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

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