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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: Q54. (page 102)

Solve each equation. Check your solution. (Lesson 2-3)
$\frac{1}{2} z + 7 = 16 鈭� \frac{3}{5} z$

Short Answer

Expert verified

The solution of the given equation is $z = \frac{90}{11}$ .

Step by step solution

01

Step 1. Write the given equation.

The given equation is 鈥� $\frac{1}{2} z + 7 = 16 鈭� \frac{3}{5} z$ 鈥�.

02

Step 2. Solve the given equation.

Solving,

$\frac{1}{2} z + 7 = 16 鈭� \frac{3}{5} z$ (Given equation)

$\frac{1}{2} z + 7 + \frac{3}{5} z = 16 鈭� \frac{3}{5} z + \frac{3}{5} z$ (Add $\frac{3}{5} z$ to both sides)

$\frac{11}{10} z + 7 = 16$ (Simplify)

$\frac{11}{10} z + 7 鈭� 7 = 16 鈭� 7$ (Subtract 7 from both sides)

$\frac{11}{10} z = 9$

$\frac{11}{10} z 脳 \frac{10}{11} = 9 脳 \frac{10}{11}$ (Multiply both sides by $\frac{10}{11}$ )

$z = \frac{90}{11}$ (Simplify)

So, $z = \frac{90}{11}$ is the solution of the given equation.

03

Step 3. Check the obtained solution.

Put $z = \frac{90}{11}$ in the given equation $\frac{1}{2} z + 7 = 16 鈭� \frac{3}{5} z$ to get,

$\begin{array}{l} \frac{1}{2} (\frac{90}{11}) + 7 = 16 鈭� \frac{3}{5} (\frac{90}{11}) \\ \frac{45}{11} + 7 = 16 鈭� 3 (\frac{18}{11}) \\ \frac{45 + 77}{11} = 16 鈭� \frac{54}{11} \\ \frac{122}{11} = \frac{176 鈭� 54}{11} \\ \frac{122}{11} = \frac{122}{11} \end{array}$

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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