Multiplying Both Sides by 10x

Oct 13, 2025 by recoveryshake.com 26 views

Understanding the Problem

To solve the given equation, we need to isolate the variable x. The equation involves fractions, so we will start by simplifying and combining the terms.

Simplifying the Equation

The given equation is:

\frac{3}{2}=\frac{3}{2x}-\frac{6}{5x}

To simplify the equation, we can start by finding a common denominator for the fractions on the right-hand side. The least common multiple of 2x and 5x is 10x.

Multiplying Both Sides by 10x

Multiplying both sides of the equation by 10x will eliminate the fractions:

10x \cdot \frac{3}{2} = 10x \cdot \left(\frac{3}{2x}-\frac{6}{5x}\right)

This simplifies to:

15x = 10x \cdot \frac{3}{2x} - 10x \cdot \frac{6}{5x}

Combining Like Terms

Now, we can combine the like terms on the right-hand side:

15x = 15 - 12x

Isolating the Variable x

To isolate the variable x, we can add 12x to both sides of the equation:

15x + 12x = 15

This simplifies to:

27x = 15

Solving for x

Finally, we can solve for x by dividing both sides of the equation by 27:

x = \frac{15}{27}

Simplifying the Fraction

The fraction $\frac{15}{27}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3:

x = \frac{5}{9}

Conclusion

Therefore, the solution to the equation $$\frac{3}{2}=\frac{3}{2x}-\frac{6}{5x}$$ is $x = \frac{5}{9}$ .

Answer

The correct answer is:

B. $x = \frac{5}{9}$

Q: What is the first step in solving the equation $$\frac{3}{2}=\frac{3}{2x}-\frac{6}{5x}$$?

A: The first step in solving the equation is to simplify and combine the terms on the right-hand side by finding a common denominator.

Q: What is the common denominator for the fractions on the right-hand side of the equation?

A: The least common multiple of 2x and 5x is 10x, which is the common denominator for the fractions on the right-hand side.

Q: How do you eliminate the fractions in the equation?

A: To eliminate the fractions, we can multiply both sides of the equation by the common denominator, which is 10x.

Q: What is the result of multiplying both sides of the equation by 10x?

A: Multiplying both sides of the equation by 10x results in:

15x = 10x \cdot \frac{3}{2x} - 10x \cdot \frac{6}{5x}

Q: How do you simplify the equation further?

A: We can simplify the equation further by combining the like terms on the right-hand side.

Q: What is the result of combining the like terms on the right-hand side?

A: Combining the like terms on the right-hand side results in:

15x = 15 - 12x

Q: How do you isolate the variable x?

A: To isolate the variable x, we can add 12x to both sides of the equation.

Q: What is the result of adding 12x to both sides of the equation?

A: Adding 12x to both sides of the equation results in:

15x + 12x = 15

Q: How do you simplify the equation further?

A: We can simplify the equation further by combining the like terms on the left-hand side.

Q: What is the result of combining the like terms on the left-hand side?

A: Combining the like terms on the left-hand side results in:

27x = 15

Q: How do you solve for x?

A: To solve for x, we can divide both sides of the equation by 27.

Q: What is the result of dividing both sides of the equation by 27?

A: Dividing both sides of the equation by 27 results in:

x = \frac{15}{27}

Q: How do you simplify the fraction?

A: We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3.

Q: What is the simplified fraction?

A: The simplified fraction is:

x = \frac{5}{9}

Q: What is the solution to the equation $$\frac{3}{2}=\frac{3}{2x}-\frac{6}{5x}$$?

A: The solution to the equation is $x = \frac{5}{9}$ .

Q: What is the correct answer?

A: The correct answer is:

B. $x = \frac{5}{9}$