Solve 1/4x-2=1/2(x-1)

$$\frac { 1 } { 4 } x - 2 = \frac { 1 } { 2 } ( x - 1 )$$

Solve for x

$$x=-6$$

Steps for Solving Linear Equation

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

$$\frac{1}{4}x-2=\frac{1}{2}x+\frac{1}{2}\left(-1\right)$$

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

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

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

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

Combine \frac{1}{4}x and -\frac{1}{2}x to get -\frac{1}{4}x.

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

Add 2 to both sides.

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

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

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

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

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

Add -1 and 4 to get 3.

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

Multiply both sides by -4, the reciprocal of -\frac{1}{4}.

$$x=\frac{3}{2}\left(-4\right)$$

Express \frac{3}{2}\left(-4\right) as a single fraction.

$$x=\frac{3\left(-4\right)}{2}$$

Multiply 3 and -4 to get -12.

$$x=\frac{-12}{2}$$

Divide -12 by 2 to get -6.

$$x=-6$$