Chapter 2: Q51. (page 102)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Write the given equation.

The given equation is “ $\frac{4}{5} x + 7 = \frac{3}{15} x - 3$ ”.

Step 2. Solve the given equation.

Solving,

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

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

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

$\frac{3}{5} x + 7 = - 3$ (Simplify)

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

$\frac{3}{5} x = - 10$ (Simplify)

$\frac{3}{5} x \times \frac{5}{3} = - 10 \times \frac{5}{3}$ (Multiply both sides by $\frac{5}{3}$ )

$x = - \frac{50}{3}$ (Simplify)

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

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

Step 3. Check the obtained solution.

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

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

On further simplification,

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

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

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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Solve 45x+7=315x−3−1623−1449−623-10

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

Probability and Statistics

Decision Maths

Mechanics Maths

Geometry

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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