Solve for x 7/(8x)-3/5=3

Add ${\displaystyle \frac{3}{5}}$ to both sides of the equation.

To write ${\displaystyle 3}$ as a fraction with a common denominator, multiply by ${\displaystyle \frac{5}{5}}$.

Combine ${\displaystyle 3}$ and ${\displaystyle \frac{5}{5}}$.

Combine the numerators over the common denominator.

Simplify the numerator.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

Since ${\displaystyle 8x,5}$ contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part ${\displaystyle 8,5}$ then find LCM for the variable part ${\displaystyle x^1}$.

The LCM is the smallest positive number that all of the numbers divide into evenly.

The prime factors for ${\displaystyle 8}$ are ${\displaystyle 2\cdot 2\cdot 2}$.

Since ${\displaystyle 5}$ has no factors besides ${\displaystyle 1}$ and ${\displaystyle 5}$.

The LCM of ${\displaystyle 8,5}$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

Multiply ${\displaystyle 2\cdot 2\cdot 2\cdot 5}$.

The factor for ${\displaystyle x^1}$ is ${\displaystyle x}$ itself.

The LCM of ${\displaystyle x^1}$ is the result of multiplying all prime factors the greatest number of times they occur in either term.

The LCM for ${\displaystyle 8x,5}$ is the numeric part ${\displaystyle 40}$ multiplied by the variable part.

Multiply each term in ${\displaystyle \frac{7}{8x}=\frac{18}{5}}$ by ${\displaystyle 40x}$.

Simplify the left side.

Simplify the right side.

Rewrite the equation as ${\displaystyle 144x=35}$.

Divide each term in ${\displaystyle 144x=35}$ by ${\displaystyle 144}$ and simplify.