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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: Q14. (page 100)

Solve each equation. Check your solution.
$\frac{b 鈭� 4}{6} = \frac{b}{2}$

Short Answer

Expert verified

The solution of the given equation is $b = 鈭� 2$ .

Step by step solution

01

Step 1. Write the given equation.

The given equation is 鈥� $\frac{b 鈭� 4}{6} = \frac{b}{2}$ 鈥�.

02

Step 2. Solve the given equation.

Solving,

$\frac{b 鈭� 4}{6} = \frac{b}{2}$ (Given equation)

$2 (b 鈭� 4) = 6 b$ (Cross-multiply)

$2 b 鈭� 8 = 6 b$ (Distributive property)

$2 b 鈭� 8 鈭� 2 b = 6 b 鈭� 2 b$ (Subtract $2 b$ from both sides)

$鈭� 8 = 4 b$ (Simplify)

$\frac{鈭� 8}{4} = \frac{4 b}{4}$ (Divide both sides by 4)

$鈭� 2 = b$ (Simplify)

$b = 鈭� 2$ (Write the variable on the left-hand side)

So, $b = 鈭� 2$ is the solution of the given equation.

03

Step 3. Check the obtained solution.

Put $b = 鈭� 2$ in the given equation $\frac{b 鈭� 4}{6} = \frac{b}{2}$ to get,

$\begin{array}{l} \frac{鈭� 2 鈭� 4}{6} = \frac{鈭� 2}{2} \\ \frac{鈭� 6}{6} = 鈭� 1 \\ 鈭� 1 = 鈭� 1 \end{array}$

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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