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

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

Solve for x

$$x = \frac{17}{4} = 4\frac{1}{4} = 4.25$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

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

To find the opposite of x-\frac{1}{2}, find the opposite of each term.

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

The opposite of -\frac{1}{2} is \frac{1}{2}.

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

Combine 4x and -x to get 3x.

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

Divide each term of x+3 by 2 to get \frac{1}{2}x+\frac{3}{2}.

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

To find the opposite of \frac{1}{2}x+\frac{3}{2}, find the opposite of each term.

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

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

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

Use the distributive property to multiply -6 by \frac{1}{2}x-\frac{3}{2}.

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

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

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

Divide -6 by 2 to get -3.

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

Express -6\left(-\frac{3}{2}\right) as a single fraction.

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

Multiply -6 and -3 to get 18.

$$3x+\frac{1}{2}=4x-3x+\frac{18}{2}$$

Divide 18 by 2 to get 9.

$$3x+\frac{1}{2}=4x-3x+9$$

Combine 4x and -3x to get x.

$$3x+\frac{1}{2}=x+9$$

Subtract x from both sides.

$$3x+\frac{1}{2}-x=9$$

Combine 3x and -x to get 2x.

$$2x+\frac{1}{2}=9$$

Subtract \frac{1}{2} from both sides.

$$2x=9-\frac{1}{2}$$

Convert 9 to fraction \frac{18}{2}.

$$2x=\frac{18}{2}-\frac{1}{2}$$

Since \frac{18}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$2x=\frac{18-1}{2}$$

Subtract 1 from 18 to get 17.

$$2x=\frac{17}{2}$$

Divide both sides by 2.

$$x=\frac{\frac{17}{2}}{2}$$

Express \frac{\frac{17}{2}}{2} as a single fraction.

$$x=\frac{17}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$x=\frac{17}{4}$$