Q51. Solve 45x+7=315x鈭�3鈭�1623鈭�14... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 2: Q51. (page 102)

Solve $\frac{4}{5} x + 7 = \frac{3}{15} x 鈭� 3$
$鈭� 16 \frac{2}{3}$
$鈭� 14 \frac{4}{9}$
$鈭� 6 \frac{2}{3}$
$- 10$

Short Answer

Expert verified

The solution of the given equation is $x = 鈭� 16 \frac{2}{3}$ . The correct option is A.

Step by step solution

Step 1. Write the given equation.

The given equation is 鈥� $\frac{4}{5} x + 7 = \frac{3}{15} x 鈭� 3$ 鈥�.

Step 2. Solve the given equation.

Solving,

$\frac{4}{5} x + 7 = \frac{3}{15} x 鈭� 3$ (Given equation)

$\frac{4}{5} x + 7 = \frac{1}{5} x 鈭� 3$ (Simplify)

$\frac{4}{5} x + 7 鈭� \frac{1}{5} x = \frac{1}{5} x 鈭� 3 鈭� \frac{1}{5} x$ (Subtract $\frac{1}{5} x$ from both sides)

$\frac{3}{5} x + 7 = 鈭� 3$ (Simplify)

$\frac{3}{5} x + 7 鈭� 7 = 鈭� 3 鈭� 7$ (Subtract 7 from both sides)

$\frac{3}{5} x = 鈭� 10$ (Simplify)

$\frac{3}{5} x 脳 \frac{5}{3} = 鈭� 10 脳 \frac{5}{3}$ (Multiply both sides by $\frac{5}{3}$ )

$x = 鈭� \frac{50}{3}$ (Simplify)

$x = 鈭� 16 \frac{2}{3}$ (Convert to mixed fraction)

So, $x = 鈭� 16 \frac{2}{3}$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $x = 鈭� 16 \frac{2}{3}$ in the given equation $\frac{4}{5} x + 7 = \frac{3}{15} x 鈭� 3$ to get,

$\begin{array}{l} \frac{4}{5} (鈭� 16 \frac{2}{3}) + 7 = \frac{3}{15} (鈭� 16 \frac{2}{3}) 鈭� 3 \\ \frac{4}{5} (鈭� \frac{50}{3}) + 7 = \frac{1}{5} (鈭� \frac{50}{3}) 鈭� 3 \\ 4 (鈭� \frac{10}{3}) + 7 = (鈭� \frac{10}{3}) 鈭� 3 \\ 鈭� \frac{40}{3} + 7 = 鈭� \frac{10}{3} 鈭� 3 \end{array}$

On further simplification,

$\begin{array}{l} \frac{鈭� 40 + 21}{3} = \frac{鈭� 10 鈭� 9}{3} \\ \frac{鈭� 19}{3} = \frac{鈭� 19}{3} \end{array}$

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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91影视

Solve $\frac{4}{5} x + 7 = \frac{3}{15} x 鈭� 3$
$鈭� 16 \frac{2}{3}$
$鈭� 14 \frac{4}{9}$
$鈭� 6 \frac{2}{3}$
$- 10$

Short Answer

Step by step solution

Step 1. Write the given equation.

Step 2. Solve the given equation.

Step 3. Check the obtained solution.

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91影视

Solve 45x+7=315x鈭�3鈭�1623鈭�1449鈭�623-10

Short Answer

Step by step solution

Step 1. Write the given equation.

Step 2. Solve the given equation.

Step 3. Check the obtained solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Applied Mathematics

Theoretical and Mathematical Physics

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve $\frac{4}{5} x + 7 = \frac{3}{15} x 鈭� 3$
$鈭� 16 \frac{2}{3}$
$鈭� 14 \frac{4}{9}$
$鈭� 6 \frac{2}{3}$
$- 10$