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

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

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Subtract \frac{3}{2}x from both sides.

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

Combine \frac{1}{3}x and -\frac{3}{2}x to get -\frac{7}{6}x.

$$-\frac{7}{6}x-\frac{1}{2}=-4$$

Add \frac{1}{2} to both sides.

$$-\frac{7}{6}x=-4+\frac{1}{2}$$

Convert -4 to fraction -\frac{8}{2}.

$$-\frac{7}{6}x=-\frac{8}{2}+\frac{1}{2}$$

Since -\frac{8}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$-\frac{7}{6}x=\frac{-8+1}{2}$$

Add -8 and 1 to get -7.

$$-\frac{7}{6}x=-\frac{7}{2}$$

Multiply both sides by -\frac{6}{7}, the reciprocal of -\frac{7}{6}.

$$x=-\frac{7}{2}\left(-\frac{6}{7}\right)$$

Multiply -\frac{7}{2} times -\frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-7\left(-6\right)}{2\times 7}$$

Do the multiplications in the fraction \frac{-7\left(-6\right)}{2\times 7}.

$$x=\frac{42}{14}$$

Divide 42 by 14 to get 3.

$$x=3$$