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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 2: Q36. (page 100)

Solve each equation. Check your solution.
$5 [2 p 鈭� 4 (p + 5)] = 25$

Short Answer

Expert verified

The solution of the given equation is $p = 鈭� \frac{25}{2}$ .

Step by step solution

01

Step 1. Write the given equation.

The given equation is 鈥� $5 [2 p 鈭� 4 (p + 5)] = 25$ 鈥�.

02

Step 2. Solve the given equation.

Solving,

$5 [2 p 鈭� 4 (p + 5)] = 25$ (Given equation)

$\frac{5 [2 p 鈭� 4 (p + 5)]}{5} = \frac{25}{5}$ (Divide both sides by 5)

$2 p 鈭� 4 (p + 5) = 5$ (Simplify)

$2 p 鈭� 4 p 鈭� 20 = 5$ (Distributive property)

$鈭� 2 p 鈭� 20 = 5$ (Simplify)

$鈭� 2 p 鈭� 20 + 20 = 5 + 20$ (Add 20 to both sides)

$鈭� 2 p = 25$ (Simplify)

$\frac{鈭� 2 p}{鈭� 2} = \frac{25}{鈭� 2}$ (Divide both sides by $- 2$ )

$p = 鈭� \frac{25}{2}$ (Simplify)

So, $p = 鈭� \frac{25}{2}$ is the solution of the given equation.

03

Step 3. Check the obtained solution.

Put $p = 鈭� \frac{25}{2}$ in the given equation $5 [2 p 鈭� 4 (p + 5)] = 25$ to get,

$\begin{array}{l} 5 [2 (鈭� \frac{25}{2}) 鈭� 4 (鈭� \frac{25}{2} + 5)] = 25 \\ 5 [鈭� 25 鈭� 4 (\frac{10 鈭� 25}{2})] = 25 \\ 5 [鈭� 25 鈭� 4 (鈭� \frac{15}{2})] = 25 \\ 5 [鈭� 25 鈭� 2 (鈭� 15)] = 25 \end{array}$

On further simplification,

$\begin{array}{l} 5 [鈭� 25 + 30] = 25 \\ 5 [5] = 25 \\ 25 = 25 \end{array}$

Since the value obtained on the left-hand side and right-hand side are equal, the obtained value is indeed a solution of the given equation.

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