Solve 3*(2x-1/3-1-2x/2)=2-x/3-1+x

$$3 \cdot ( \frac { 2 x - 1 } { 3 } - \frac { 1 - 2 x } { 2 } ) = \frac { 2 - x } { 3 } - 1 + x$$

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$18\left(\frac{2x-1}{3}-\frac{1-2x}{2}\right)=2\left(2-x\right)-6+6x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{2x-1}{3} times \frac{2}{2}. Multiply \frac{1-2x}{2} times \frac{3}{3}.

$$18\left(\frac{2\left(2x-1\right)}{6}-\frac{3\left(1-2x\right)}{6}\right)=2\left(2-x\right)-6+6x$$

Since \frac{2\left(2x-1\right)}{6} and \frac{3\left(1-2x\right)}{6} have the same denominator, subtract them by subtracting their numerators.

$$18\times \frac{2\left(2x-1\right)-3\left(1-2x\right)}{6}=2\left(2-x\right)-6+6x$$

Do the multiplications in 2\left(2x-1\right)-3\left(1-2x\right).

$$18\times \frac{4x-2-3+6x}{6}=2\left(2-x\right)-6+6x$$

Combine like terms in 4x-2-3+6x.

$$18\times \frac{10x-5}{6}=2\left(2-x\right)-6+6x$$

Cancel out 6, the greatest common factor in 18 and 6.

$$3\left(10x-5\right)=2\left(2-x\right)-6+6x$$

Use the distributive property to multiply 3 by 10x-5.

$$30x-15=2\left(2-x\right)-6+6x$$

Use the distributive property to multiply 2 by 2-x.

$$30x-15=4-2x-6+6x$$

Subtract 6 from 4 to get -2.

$$30x-15=-2-2x+6x$$

Combine -2x and 6x to get 4x.

$$30x-15=-2+4x$$

Subtract 4x from both sides.

$$30x-15-4x=-2$$

Combine 30x and -4x to get 26x.

$$26x-15=-2$$

Add 15 to both sides.

$$26x=-2+15$$

Add -2 and 15 to get 13.

$$26x=13$$

Divide both sides by 26.

$$x=\frac{13}{26}$$

Reduce the fraction \frac{13}{26} to lowest terms by extracting and canceling out 13.

$$x=\frac{1}{2}$$