Solve 7/2-x-5/2x-1=3/2

$$\frac{ 7 }{ 2 } - \frac{ x-5 }{ 2x-1 } = \frac{ 3 }{ 2 }$$

Solve for x

$$x=-1$$

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 2\left(2x-1\right), the least common multiple of 2,2x-1.

$$2\left(2x-1\right)\times \frac{7}{2}-2\left(x-5\right)=3\left(2x-1\right)$$

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

$$\left(4x-2\right)\times \frac{7}{2}-2\left(x-5\right)=3\left(2x-1\right)$$

Use the distributive property to multiply 4x-2 by \frac{7}{2}.

$$14x-7-2\left(x-5\right)=3\left(2x-1\right)$$

Use the distributive property to multiply -2 by x-5.

$$14x-7-2x+10=3\left(2x-1\right)$$

Combine 14x and -2x to get 12x.

$$12x-7+10=3\left(2x-1\right)$$

Add -7 and 10 to get 3.

$$12x+3=3\left(2x-1\right)$$

Use the distributive property to multiply 3 by 2x-1.

$$12x+3=6x-3$$

Subtract 6x from both sides.

$$12x+3-6x=-3$$

Combine 12x and -6x to get 6x.

$$6x+3=-3$$

Subtract 3 from both sides.

$$6x=-3-3$$

Subtract 3 from -3 to get -6.

$$6x=-6$$

Divide both sides by 6.

$$x=\frac{-6}{6}$$

Divide -6 by 6 to get -1.

$$x=-1$$