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

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

Solve for x

$$x=\frac{1}{3}\approx 0.333333333$$

Steps for Solving Linear Equation

Add 3x to both sides.

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

Combine \frac{3}{2}x and 3x to get \frac{9}{2}x.

$$\frac{9}{2}x-1=\frac{1}{2}$$

Add 1 to both sides.

$$\frac{9}{2}x=\frac{1}{2}+1$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{9}{2}x=\frac{1}{2}+\frac{2}{2}$$

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

$$\frac{9}{2}x=\frac{1+2}{2}$$

Add 1 and 2 to get 3.

$$\frac{9}{2}x=\frac{3}{2}$$

Multiply both sides by \frac{2}{9}, the reciprocal of \frac{9}{2}.

$$x=\frac{3}{2}\times \frac{2}{9}$$

Multiply \frac{3}{2} times \frac{2}{9} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{3\times 2}{2\times 9}$$

Cancel out 2 in both numerator and denominator.

$$x=\frac{3}{9}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

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