Question

Уравнение: x / x + 4 = 6/10

Answer 1

X / (x + 4) = 6/10

10 x = 6 x + 24

10 x - 6 x = 24

4 x = 24

x = 6

Answer 2

To solve the equation $\frac{x}{x+4} = \frac{6}{10}$, we need to find the value of $x$ that satisfies the equation. To do that, we can follow these steps:

Step 1: Clear the fraction by multiplying both sides by $(x + 4)$ to eliminate the denominator.

$\frac{x}{x+4} \times (x + 4) = \frac{6}{10} \times (x + 4)$

Step 2: Simplify both sides.

$x = \frac{6}{10} \times (x + 4)$

Step 3: Distribute the $\frac{6}{10}$ on the right side.

$x = \frac{3}{5} \times (x + 4)$

Step 4: Expand the right side.

$x = \frac{3x}{5} + \frac{12}{5}$

Step 5: Move all terms containing $x$ to one side of the equation, and constant terms to the other side.

$x - \frac{3x}{5} = \frac{12}{5}$

Step 6: Find a common denominator for the terms on the left side.

$\frac{5x}{5} - \frac{3x}{5} = \frac{12}{5}$

Step 7: Combine like terms.

$\frac{2x}{5} = \frac{12}{5}$

Step 8: Now, isolate $x$ by multiplying both sides by the reciprocal of $\frac{2}{5}$, which is $\frac{5}{2}$.

$x = \frac{12}{5} \times \frac{5}{2}$

Step 9: Simplify the right side.

$x = 6$

So, the solution to the equation is $x = 6$.