Solve 1/6x-2=1/2x-3/2

$$\frac{ 1 }{ 6 } x-2= \frac{ 1 }{ 2 } x- \frac{ 3 }{ 2 }$$

Solve for x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps for Solving Linear Equation

Subtract \frac{1}{2}x from both sides.

$$\frac{1}{6}x-2-\frac{1}{2}x=-\frac{3}{2}$$

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

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

Add 2 to both sides.

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

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

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

Since -\frac{3}{2} and \frac{4}{2} have the same denominator, add them by adding their numerators.

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

Add -3 and 4 to get 1.

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

Multiply both sides by -3, the reciprocal of -\frac{1}{3}.

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

Multiply \frac{1}{2} and -3 to get \frac{-3}{2}.

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

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

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