Solve (8/15)^3-(1/3)^3-(1/5)^3=x/75

$$( \frac { 8 } { 15 } ) ^ { 3 } - ( \frac { 1 } { 3 } ) ^ { 3 } - ( \frac { 1 } { 5 } ) ^ { 3 } = \frac { x } { 75 }$$

Solve for x

$$x=8$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 75.

$$75\left(\left(\frac{8}{15}\right)^{3}-\left(\frac{1}{3}\right)^{3}\right)-75\times \left(\frac{1}{5}\right)^{3}=x$$

Calculate \frac{8}{15} to the power of 3 and get \frac{512}{3375}.

$$75\left(\frac{512}{3375}-\left(\frac{1}{3}\right)^{3}\right)-75\times \left(\frac{1}{5}\right)^{3}=x$$

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$75\left(\frac{512}{3375}-\frac{1}{27}\right)-75\times \left(\frac{1}{5}\right)^{3}=x$$

Least common multiple of 3375 and 27 is 3375. Convert \frac{512}{3375} and \frac{1}{27} to fractions with denominator 3375.

$$75\left(\frac{512}{3375}-\frac{125}{3375}\right)-75\times \left(\frac{1}{5}\right)^{3}=x$$

Since \frac{512}{3375} and \frac{125}{3375} have the same denominator, subtract them by subtracting their numerators.

$$75\times \frac{512-125}{3375}-75\times \left(\frac{1}{5}\right)^{3}=x$$

Subtract 125 from 512 to get 387.

$$75\times \frac{387}{3375}-75\times \left(\frac{1}{5}\right)^{3}=x$$

Reduce the fraction \frac{387}{3375} to lowest terms by extracting and canceling out 9.

$$75\times \frac{43}{375}-75\times \left(\frac{1}{5}\right)^{3}=x$$

Express 75\times \frac{43}{375} as a single fraction.

$$\frac{75\times 43}{375}-75\times \left(\frac{1}{5}\right)^{3}=x$$

Multiply 75 and 43 to get 3225.

$$\frac{3225}{375}-75\times \left(\frac{1}{5}\right)^{3}=x$$

Reduce the fraction \frac{3225}{375} to lowest terms by extracting and canceling out 75.

$$\frac{43}{5}-75\times \left(\frac{1}{5}\right)^{3}=x$$

Calculate \frac{1}{5} to the power of 3 and get \frac{1}{125}.

$$\frac{43}{5}-75\times \frac{1}{125}=x$$

Multiply 75 and \frac{1}{125} to get \frac{75}{125}.

$$\frac{43}{5}-\frac{75}{125}=x$$

Reduce the fraction \frac{75}{125} to lowest terms by extracting and canceling out 25.

$$\frac{43}{5}-\frac{3}{5}=x$$

Since \frac{43}{5} and \frac{3}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{43-3}{5}=x$$

Subtract 3 from 43 to get 40.

$$\frac{40}{5}=x$$

Divide 40 by 5 to get 8.

$$8=x$$

Swap sides so that all variable terms are on the left hand side.

$$x=8$$