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.
$7 (2 p + 1) = 14 p + 7$

The solution for the equation $7 (2 p + 1) = 14 p + 7$ is all real numbers.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1 – Use distributive property

The distributive property is given as $a (b + c) = a b + a c$ .

The given equation is $7 (2 p + 1) = 14 p + 7$ .

So,

$\begin{matrix} 7 (2 p + 1) = 14 p + 7 \\ 14 p + 7 = 14 p + 7 (Use distributive property) \end{matrix}$

Step 2 – Combine the like terms

Combine the like terms.

$\begin{matrix} 14 p - 14 p + 7 = 14 p - 14 p + 7 (subtract 14p from both sides) \\ 7 - 7 = 0 + 7 - 7 (subtract 7 from both sides) \\ 0 = 0 (simplify) \end{matrix}$

Since $0 = 0$ is true, the solution of the equation are all real numbers.

Step 3 – Check the solution

To check the solution, choose any real number as a value of p and substitute in the equation $7 (2 p + 1) = 14 p + 7$ .

Choose $p = 2$ .

Then, substitute $p = 2$ in $7 (2 p + 1) = 14 p + 7$ and check the result.

$\begin{matrix} 7 (2 \times 2 + 1) = 14 \times 2 + 7 \\ 7 (4 + 1) = 28 + 7 \\ 7 \times 5 = 28 + 7 \\ 35 = 35 \end{matrix}$

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

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Pre-algebra

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Short Answer

Solve the equation. Check your solution.
$7 (2 p + 1) = 14 p + 7$

Step by Step Solution

Step 1 – Use distributive property

Step 2 – Combine the like terms

Step 3 – Check the solution

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Solve the equation. Check your solution.72p+1=14p+7

Step by Step Solution

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Solve the equation. Check your solution.
$7 (2 p + 1) = 14 p + 7$