Solve x-3x/5-(1/2)(x-3x/5)=10

$$x- \frac{ 3x }{ 5 } -( \frac{ 1 }{ 2 } )(x- \frac{ 3x }{ 5 } )=10$$

Solve for x

$$x=50$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 5,2.

$$10\left(x-\frac{3x}{5}\right)-5\left(x-\frac{3x}{5}\right)=100$$

Use the distributive property to multiply 10 by x-\frac{3x}{5}.

$$10x+10\left(-\frac{3x}{5}\right)-5\left(x-\frac{3x}{5}\right)=100$$

Cancel out 5, the greatest common factor in 10 and 5.

$$10x-2\times 3x-5\left(x-\frac{3x}{5}\right)=100$$

Multiply -2 and 3 to get -6.

$$10x-6x-5\left(x-\frac{3x}{5}\right)=100$$

Combine 10x and -6x to get 4x.

$$4x-5\left(x-\frac{3x}{5}\right)=100$$

Multiply both sides of the equation by 5.

$$20x-25\left(x-\frac{3x}{5}\right)=500$$

Multiply both sides of the equation by 5.

$$100x-5\times 25\left(x-\frac{3x}{5}\right)=2500$$

Multiply -5 and 25 to get -125.

$$100x-125\left(x-\frac{3x}{5}\right)=2500$$

Use the distributive property to multiply -125 by x-\frac{3x}{5}.

$$100x-125x+125\times \frac{3x}{5}=2500$$

Cancel out 5, the greatest common factor in 125 and 5.

$$100x-125x+25\times 3x=2500$$

Multiply 25 and 3 to get 75.

$$100x-125x+75x=2500$$

Combine -125x and 75x to get -50x.

$$100x-50x=2500$$

Combine 100x and -50x to get 50x.

$$50x=2500$$

Divide both sides by 50.

$$x=\frac{2500}{50}$$

Divide 2500 by 50 to get 50.

$$x=50$$