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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: Q37. (page 94)

Solve each equation. Check your solution.
$\frac{5}{6} k + \frac{2}{3} = \frac{4}{3}$

Short Answer

Expert verified

The solution of the given equation is $k = \frac{4}{5}$ .

Step by step solution

01

Step 1. Write the given equation.

The given equation is 鈥� $\frac{5}{6} k + \frac{2}{3} = \frac{4}{3}$ 鈥�.

02

Step 2. Solve the given equation.

Solving,

$\frac{5}{6} k + \frac{2}{3} = \frac{4}{3}$ (Given equation)

$\frac{5}{6} k + \frac{2}{3} 鈭� \frac{2}{3} = \frac{4}{3} 鈭� \frac{2}{3}$ (Subtract $\frac{2}{3}$ from both sides)

$\frac{5}{6} k = \frac{2}{3}$ (Simplify)

$\frac{5}{6} k 脳 \frac{6}{5} = \frac{2}{3} 脳 \frac{6}{5}$ (Multiply both sides by $\frac{6}{5}$ )

$k = \frac{4}{5}$ (Simplify)

So, $k = \frac{4}{5}$ is the solution of the given equation.

03

Step 3. Check the obtained solution.

Put $k = \frac{4}{5}$ in the given equation $\frac{5}{6} k + \frac{2}{3} = \frac{4}{3}$ to get,

$\begin{array}{l} \frac{5}{6} (\frac{4}{5}) + \frac{2}{3} = \frac{4}{3} \\ \frac{2}{3} + \frac{2}{3} = \frac{4}{3} \\ \frac{4}{3} = \frac{4}{3} \end{array}$

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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