Solve (3-x/2)-(1-x/3)=7-(x-x/2)

$$( 3 - \frac { x } { 2 } ) - ( 1 - \frac { x } { 3 } ) = 7 - ( x - \frac { x } { 2 } )$$

Solve for x

$$x=15$$

Steps for Solving Linear Equation

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

$$6\left(3-\frac{x}{2}\right)-6\left(1-\frac{x}{3}\right)=42-6\left(x-\frac{x}{2}\right)$$

Use the distributive property to multiply 6 by 3-\frac{x}{2}.

$$18+6\left(-\frac{x}{2}\right)-6\left(1-\frac{x}{3}\right)=42-6\left(x-\frac{x}{2}\right)$$

Cancel out 2, the greatest common factor in 6 and 2.

$$18-3x-6\left(1-\frac{x}{3}\right)=42-6\left(x-\frac{x}{2}\right)$$

Combine x and -\frac{x}{2} to get \frac{1}{2}x.

$$18-3x-6\left(1-\frac{x}{3}\right)=42-6\times \frac{1}{2}x$$

Multiply 6 and \frac{1}{2} to get \frac{6}{2}.

$$18-3x-6\left(1-\frac{x}{3}\right)=42-\frac{6}{2}x$$

Divide 6 by 2 to get 3.

$$18-3x-6\left(1-\frac{x}{3}\right)=42-3x$$

Add 3x to both sides.

$$18-3x-6\left(1-\frac{x}{3}\right)+3x=42$$

Multiply both sides of the equation by 3.

$$3\left(18-3x-6\left(1-\frac{x}{3}\right)\right)+9x=126$$

Multiply both sides of the equation by 3.

$$9\left(18-3x-6\left(1-\frac{x}{3}\right)\right)+27x=378$$

Use the distributive property to multiply -6 by 1-\frac{x}{3}.

$$9\left(18-3x-6+6\times \frac{x}{3}\right)+27x=378$$

Cancel out 3, the greatest common factor in 6 and 3.

$$9\left(18-3x-6+2x\right)+27x=378$$

Subtract 6 from 18 to get 12.

$$9\left(12-3x+2x\right)+27x=378$$

Combine -3x and 2x to get -x.

$$9\left(12-x\right)+27x=378$$

Use the distributive property to multiply 9 by 12-x.

$$108-9x+27x=378$$

Combine -9x and 27x to get 18x.

$$108+18x=378$$

Subtract 108 from both sides.

$$18x=378-108$$

Subtract 108 from 378 to get 270.

$$18x=270$$

Divide both sides by 18.

$$x=\frac{270}{18}$$

Divide 270 by 18 to get 15.

$$x=15$$