Solve 1/5x-2=1/2(x-1)

$$\frac{ 1 }{ 5 } x-2= \frac{ 1 }{ 2 } (x-1)$$

Solve for x

$$x=-5$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by x-1.

$$\frac{1}{5}x-2=\frac{1}{2}x+\frac{1}{2}\left(-1\right)$$

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

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

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

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

Combine \frac{1}{5}x and -\frac{1}{2}x to get -\frac{3}{10}x.

$$-\frac{3}{10}x-2=-\frac{1}{2}$$

Add 2 to both sides.

$$-\frac{3}{10}x=-\frac{1}{2}+2$$

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

$$-\frac{3}{10}x=-\frac{1}{2}+\frac{4}{2}$$

Since -\frac{1}{2} and \frac{4}{2} have the same denominator, add them by adding their numerators.

$$-\frac{3}{10}x=\frac{-1+4}{2}$$

Add -1 and 4 to get 3.

$$-\frac{3}{10}x=\frac{3}{2}$$

Multiply both sides by -\frac{10}{3}, the reciprocal of -\frac{3}{10}.

$$x=\frac{3}{2}\left(-\frac{10}{3}\right)$$

Multiply \frac{3}{2} times -\frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{3\left(-10\right)}{2\times 3}$$

Cancel out 3 in both numerator and denominator.

$$x=\frac{-10}{2}$$

Divide -10 by 2 to get -5.

$$x=-5$$