Solve x^3-x^3=50-x/2x-1

$${ x }^{ 3 } - { x }^{ 3 } = \frac{ 50-x }{ 2x-1 }$$

Solve for x

$$x=50$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 2x-1.

$$\left(2x-1\right)x^{3}-x^{3}\left(2x-1\right)=50-x$$

Use the distributive property to multiply 2x-1 by x^{3}.

$$2x^{4}-x^{3}-x^{3}\left(2x-1\right)=50-x$$

Use the distributive property to multiply -x^{3} by 2x-1.

$$2x^{4}-x^{3}-2x^{4}+x^{3}=50-x$$

Combine 2x^{4} and -2x^{4} to get 0.

$$-x^{3}+x^{3}=50-x$$

Combine -x^{3} and x^{3} to get 0.

$$0=50-x$$

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

$$50-x=0$$

Subtract 50 from both sides. Anything subtracted from zero gives its negation.

$$-x=-50$$

Multiply both sides by -1.

$$x=50$$