Solve x-2x+x-1/5/3=1-3x-1/3-2x/5

$$x- \frac{ 2x+ \frac{ x-1 }{ 5 } }{ 3 } = 1- \frac{ 3x- \frac{ 1 }{ 3 } -2x }{ 5 }$$

Solve for x

$$x = \frac{15}{7} = 2\frac{1}{7} \approx 2.142857143$$

Steps for Solving Linear Equation

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

$$15x-5\left(2x+\frac{x-1}{5}\right)=15-3\left(3x-\frac{1}{3}-2x\right)$$

Use the distributive property to multiply -5 by 2x+\frac{x-1}{5}.

$$15x-10x-5\times \frac{x-1}{5}=15-3\left(3x-\frac{1}{3}-2x\right)$$

Express -5\times \frac{x-1}{5} as a single fraction.

$$15x-10x+\frac{-5\left(x-1\right)}{5}=15-3\left(3x-\frac{1}{3}-2x\right)$$

Cancel out 5 and 5.

$$15x-10x-\left(x-1\right)=15-3\left(3x-\frac{1}{3}-2x\right)$$

To find the opposite of x-1, find the opposite of each term.

$$15x-10x-x-\left(-1\right)=15-3\left(3x-\frac{1}{3}-2x\right)$$

The opposite of -1 is 1.

$$15x-10x-x+1=15-3\left(3x-\frac{1}{3}-2x\right)$$

Combine -10x and -x to get -11x.

$$15x-11x+1=15-3\left(3x-\frac{1}{3}-2x\right)$$

Combine 15x and -11x to get 4x.

$$4x+1=15-3\left(3x-\frac{1}{3}-2x\right)$$

Combine 3x and -2x to get x.

$$4x+1=15-3\left(x-\frac{1}{3}\right)$$

Use the distributive property to multiply -3 by x-\frac{1}{3}.

$$4x+1=15-3x-3\left(-\frac{1}{3}\right)$$

Multiply -3 times -\frac{1}{3}.

$$4x+1=15-3x+1$$

Add 15 and 1 to get 16.

$$4x+1=16-3x$$

Add 3x to both sides.

$$4x+1+3x=16$$

Combine 4x and 3x to get 7x.

$$7x+1=16$$

Subtract 1 from both sides.

$$7x=16-1$$

Subtract 1 from 16 to get 15.

$$7x=15$$

Divide both sides by 7.

$$x=\frac{15}{7}$$