which of the following represents the solution of $\frac{3}{2}=\frac{3}{2x}-\frac{6}{5x}$?\n$x =…

which of the following represents the solution of $\frac{3}{2}=\frac{3}{2x}-\frac{6}{5x}$?\n$x = \frac{1}{5}$\n$x=\frac{5}{9}$\nall real numbers\nno solution

which of the following represents the solution of $\frac{3}{2}=\frac{3}{2x}-\frac{6}{5x}$?\n$x = \frac{1}{5}$\n$x=\frac{5}{9}$\nall real numbers\nno solution

Answer

Explanation:

Step1: Find a common - denominator

The common denominator of (2x) and (5x) is (10x). Rewrite the right - hand side of the equation: (\frac{3}{2x}-\frac{6}{5x}=\frac{3\times5}{2x\times5}-\frac{6\times2}{5x\times2}=\frac{15}{10x}-\frac{12}{10x}=\frac{15 - 12}{10x}=\frac{3}{10x}). The original equation (\frac{3}{2}=\frac{3}{2x}-\frac{6}{5x}) becomes (\frac{3}{2}=\frac{3}{10x}).

Step2: Cross - multiply

Cross - multiplying gives (3\times10x = 3\times2).

Step3: Simplify the equation

(30x=6).

Step4: Solve for (x)

Divide both sides of the equation by 30: (x=\frac{6}{30}=\frac{1}{5}).

Answer:

(x = \frac{1}{5})