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

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

Solve for x

$$x = -\frac{15}{2} = -7\frac{1}{2} = -7.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 4\left(2x-1\right), the least common multiple of 4,1-2x,2.

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

Use the distributive property to multiply 4 by 2x-1.

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

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

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

Multiply 4 and 4 to get 16.

$$6x-3+16=2\left(2x-1\right)$$

Add -3 and 16 to get 13.

$$6x+13=2\left(2x-1\right)$$

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

$$6x+13=4x-2$$

Subtract 4x from both sides.

$$6x+13-4x=-2$$

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

$$2x+13=-2$$

Subtract 13 from both sides.

$$2x=-2-13$$

Subtract 13 from -2 to get -15.

$$2x=-15$$

Divide both sides by 2.

$$x=\frac{-15}{2}$$

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$x=-\frac{15}{2}$$