Solve 2x-(x+2/3-x-1/2)+3/2(1-x)=2x-3/2+frac{1}{3}*frac{x+4}{2}

$$2 x - ( \frac { x + 2 } { 3 } - \frac { x - 1 } { 2 } ) + \frac { 3 } { 2 } ( 1 - x ) = \frac { 2 x - 3 } { 2 } + \frac { 1 } { 3 } \cdot \frac { x + 4 } { 2 }$$

Solve for x

$$x = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

Steps for Solving Linear Equation

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

$$6\left(2x-\left(\frac{x+2}{3}-\frac{x-1}{2}\right)\right)+9\left(1-x\right)=3\left(2x-3\right)+1\left(x+4\right)$$

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

$$6\left(2x-\left(\frac{2\left(x+2\right)}{6}-\frac{3\left(x-1\right)}{6}\right)\right)+9\left(1-x\right)=3\left(2x-3\right)+1\left(x+4\right)$$

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

$$6\left(2x-\frac{2\left(x+2\right)-3\left(x-1\right)}{6}\right)+9\left(1-x\right)=3\left(2x-3\right)+1\left(x+4\right)$$

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

$$6\left(2x-\frac{2x+4-3x+3}{6}\right)+9\left(1-x\right)=3\left(2x-3\right)+1\left(x+4\right)$$

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

$$6\left(2x-\frac{-x+7}{6}\right)+9\left(1-x\right)=3\left(2x-3\right)+1\left(x+4\right)$$

Use the distributive property to multiply 6 by 2x-\frac{-x+7}{6}.

$$12x+6\left(-\frac{-x+7}{6}\right)+9\left(1-x\right)=3\left(2x-3\right)+1\left(x+4\right)$$

Express 6\left(-\frac{-x+7}{6}\right) as a single fraction.

$$12x+\frac{-6\left(-x+7\right)}{6}+9\left(1-x\right)=3\left(2x-3\right)+1\left(x+4\right)$$

Cancel out 6 and 6.

$$12x-\left(-x+7\right)+9\left(1-x\right)=3\left(2x-3\right)+1\left(x+4\right)$$

To find the opposite of -x+7, find the opposite of each term.

$$12x-\left(-x\right)-7+9\left(1-x\right)=3\left(2x-3\right)+1\left(x+4\right)$$

The opposite of -x is x.

$$12x+x-7+9\left(1-x\right)=3\left(2x-3\right)+1\left(x+4\right)$$

Combine 12x and x to get 13x.

$$13x-7+9\left(1-x\right)=3\left(2x-3\right)+1\left(x+4\right)$$

Use the distributive property to multiply 9 by 1-x.

$$13x-7+9-9x=3\left(2x-3\right)+1\left(x+4\right)$$

Add -7 and 9 to get 2.

$$13x+2-9x=3\left(2x-3\right)+1\left(x+4\right)$$

Combine 13x and -9x to get 4x.

$$4x+2=3\left(2x-3\right)+1\left(x+4\right)$$

Use the distributive property to multiply 3 by 2x-3.

$$4x+2=6x-9+1\left(x+4\right)$$

Use the distributive property to multiply 1 by x+4.

$$4x+2=6x-9+x+4$$

Combine 6x and x to get 7x.

$$4x+2=7x-9+4$$

Add -9 and 4 to get -5.

$$4x+2=7x-5$$

Subtract 7x from both sides.

$$4x+2-7x=-5$$

Combine 4x and -7x to get -3x.

$$-3x+2=-5$$

Subtract 2 from both sides.

$$-3x=-5-2$$

Subtract 2 from -5 to get -7.

$$-3x=-7$$

Divide both sides by -3.

$$x=\frac{-7}{-3}$$

Fraction \frac{-7}{-3} can be simplified to \frac{7}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{7}{3}$$