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

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

Solve for x

$$x = -\frac{13}{2} = -6\frac{1}{2} = -6.5$$

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 2,2x+3.

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

Use the distributive property to multiply 3 by 2x+3.

$$6x+9=2\times 2\left(x-1\right)$$

Multiply 2 and 2 to get 4.

$$6x+9=4\left(x-1\right)$$

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

$$6x+9=4x-4$$

Subtract 4x from both sides.

$$6x+9-4x=-4$$

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

$$2x+9=-4$$

Subtract 9 from both sides.

$$2x=-4-9$$

Subtract 9 from -4 to get -13.

$$2x=-13$$

Divide both sides by 2.

$$x=\frac{-13}{2}$$

Fraction \frac{-13}{2} can be rewritten as -\frac{13}{2} by extracting the negative sign.

$$x=-\frac{13}{2}$$