Solve 1/2x-2(x-3/4)=x-1/2

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

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2x-8\left(x-\frac{3}{4}\right)=2\left(x-1\right)$$

Use the distributive property to multiply -8 by x-\frac{3}{4}.

$$2x-8x-8\left(-\frac{3}{4}\right)=2\left(x-1\right)$$

Express -8\left(-\frac{3}{4}\right) as a single fraction.

$$2x-8x+\frac{-8\left(-3\right)}{4}=2\left(x-1\right)$$

Multiply -8 and -3 to get 24.

$$2x-8x+\frac{24}{4}=2\left(x-1\right)$$

Divide 24 by 4 to get 6.

$$2x-8x+6=2\left(x-1\right)$$

Combine 2x and -8x to get -6x.

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

Use the distributive property to multiply 2 by x-1.

$$-6x+6=2x-2$$

Subtract 2x from both sides.

$$-6x+6-2x=-2$$

Combine -6x and -2x to get -8x.

$$-8x+6=-2$$

Subtract 6 from both sides.

$$-8x=-2-6$$

Subtract 6 from -2 to get -8.

$$-8x=-8$$

Divide both sides by -8.

$$x=\frac{-8}{-8}$$

Divide -8 by -8 to get 1.

$$x=1$$