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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 94)

Solve each equation. Check your solution.
$鈭� \frac{5}{2} = \frac{3}{4} z + \frac{1}{2}$

Short Answer

Expert verified

The solution of the given equation is $z = 鈭� 4$ .

Step by step solution

01

Step 1. Write the given equation.

The given equation is 鈥� $鈭� \frac{5}{2} = \frac{3}{4} z + \frac{1}{2}$ 鈥�.

02

Step 2. Solve the given equation.

Solving,

$鈭� \frac{5}{2} = \frac{3}{4} z + \frac{1}{2}$ (Given equation)

$鈭� \frac{5}{2} 鈭� \frac{1}{2} = \frac{3}{4} z + \frac{1}{2} 鈭� \frac{1}{2}$ (Subtract $\frac{1}{2}$ from both sides)

$鈭� 3 = \frac{3}{4} z$ (Simplify)

$鈭� 3 脳 \frac{4}{3} = \frac{3}{4} z 脳 \frac{4}{3}$ (Multiply both sides by $\frac{4}{3}$ )

$鈭� 4 = z$ (Simplify)

$z = 鈭� 4$ (Write the variable on the left-hand side)

So, $z = 鈭� 4$ is the solution of the given equation.

03

Step 3. Check the obtained solution.

Put $z = 鈭� 4$ in the given equation $鈭� \frac{5}{2} = \frac{3}{4} z + \frac{1}{2}$ to get,

$\begin{array}{l} 鈭� \frac{5}{2} = \frac{3}{4} (鈭� 4) + \frac{1}{2} \\ 鈭� \frac{5}{2} = 3 (鈭� 1) + \frac{1}{2} \\ 鈭� \frac{5}{2} = 鈭� 3 + \frac{1}{2} \\ 鈭� \frac{5}{2} = 鈭� \frac{5}{2} \end{array}$

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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