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

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

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{3}{2} since division by zero is not defined. Multiply both sides of the equation by 2\left(2x-3\right), the least common multiple of 2x-3,2.

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

Since \frac{3}{2} and \frac{1-x}{2} have the same denominator, add them by adding their numerators.

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

Combine like terms in 3+1-x.

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

Express 2\times \frac{4-x}{2} as a single fraction.

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

Cancel out 2 and 2.

$$4-x=2x-3$$

Subtract 2x from both sides.

$$4-x-2x=-3$$

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

$$4-3x=-3$$

Subtract 4 from both sides.

$$-3x=-3-4$$

Subtract 4 from -3 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.

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