Solve 2x/3-x+4(2-3/5)=3-(x/3-5)+x

$$\frac{ 2x }{ 3 } -x+4(2- \frac{ 3 }{ 5 } )=3-( \frac{ x }{ 3 } -5)+x$$

Solve for x

$$x = -\frac{12}{5} = -2\frac{2}{5} = -2.4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5.

$$5\times 2x-15x+60\left(2-\frac{3}{5}\right)=15\left(3-\left(\frac{x}{3}-5\right)\right)+15x$$

Multiply 5 and 2 to get 10.

$$10x-15x+60\left(2-\frac{3}{5}\right)=15\left(3-\left(\frac{x}{3}-5\right)\right)+15x$$

Combine 10x and -15x to get -5x.

$$-5x+60\left(2-\frac{3}{5}\right)=15\left(3-\left(\frac{x}{3}-5\right)\right)+15x$$

Convert 2 to fraction \frac{10}{5}.

$$-5x+60\left(\frac{10}{5}-\frac{3}{5}\right)=15\left(3-\left(\frac{x}{3}-5\right)\right)+15x$$

Since \frac{10}{5} and \frac{3}{5} have the same denominator, subtract them by subtracting their numerators.

$$-5x+60\times \frac{10-3}{5}=15\left(3-\left(\frac{x}{3}-5\right)\right)+15x$$

Subtract 3 from 10 to get 7.

$$-5x+60\times \frac{7}{5}=15\left(3-\left(\frac{x}{3}-5\right)\right)+15x$$

Express 60\times \frac{7}{5} as a single fraction.

$$-5x+\frac{60\times 7}{5}=15\left(3-\left(\frac{x}{3}-5\right)\right)+15x$$

Multiply 60 and 7 to get 420.

$$-5x+\frac{420}{5}=15\left(3-\left(\frac{x}{3}-5\right)\right)+15x$$

Divide 420 by 5 to get 84.

$$-5x+84=15\left(3-\left(\frac{x}{3}-5\right)\right)+15x$$

To find the opposite of \frac{x}{3}-5, find the opposite of each term.

$$-5x+84=15\left(3-\frac{x}{3}-\left(-5\right)\right)+15x$$

The opposite of -5 is 5.

$$-5x+84=15\left(3-\frac{x}{3}+5\right)+15x$$

Add 3 and 5 to get 8.

$$-5x+84=15\left(8-\frac{x}{3}\right)+15x$$

Use the distributive property to multiply 15 by 8-\frac{x}{3}.

$$-5x+84=120-15\times \frac{x}{3}+15x$$

Cancel out 3, the greatest common factor in 15 and 3.

$$-5x+84=120-5x+15x$$

Combine -5x and 15x to get 10x.

$$-5x+84=120+10x$$

Subtract 10x from both sides.

$$-5x+84-10x=120$$

Combine -5x and -10x to get -15x.

$$-15x+84=120$$

Subtract 84 from both sides.

$$-15x=120-84$$

Subtract 84 from 120 to get 36.

$$-15x=36$$

Divide both sides by -15.

$$x=\frac{36}{-15}$$

Reduce the fraction \frac{36}{-15} to lowest terms by extracting and canceling out 3.

$$x=-\frac{12}{5}$$