Solve (x-4)-1/3(2x-9)=1/4(x-1)-2

$$( x - 4 ) - \frac { 1 } { 3 } ( 2 x - 9 ) = \frac { 1 } { 4 } ( x - 1 ) - 2$$

Solve for x

$$x=-15$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{1}{3} by 2x-9.

$$x-4-\frac{1}{3}\times 2x-\frac{1}{3}\left(-9\right)=\frac{1}{4}\left(x-1\right)-2$$

Express -\frac{1}{3}\times 2 as a single fraction.

$$x-4+\frac{-2}{3}x-\frac{1}{3}\left(-9\right)=\frac{1}{4}\left(x-1\right)-2$$

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

$$x-4-\frac{2}{3}x-\frac{1}{3}\left(-9\right)=\frac{1}{4}\left(x-1\right)-2$$

Express -\frac{1}{3}\left(-9\right) as a single fraction.

$$x-4-\frac{2}{3}x+\frac{-\left(-9\right)}{3}=\frac{1}{4}\left(x-1\right)-2$$

Multiply -1 and -9 to get 9.

$$x-4-\frac{2}{3}x+\frac{9}{3}=\frac{1}{4}\left(x-1\right)-2$$

Divide 9 by 3 to get 3.

$$x-4-\frac{2}{3}x+3=\frac{1}{4}\left(x-1\right)-2$$

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

$$\frac{1}{3}x-4+3=\frac{1}{4}\left(x-1\right)-2$$

Add -4 and 3 to get -1.

$$\frac{1}{3}x-1=\frac{1}{4}\left(x-1\right)-2$$

Use the distributive property to multiply \frac{1}{4} by x-1.

$$\frac{1}{3}x-1=\frac{1}{4}x+\frac{1}{4}\left(-1\right)-2$$

Multiply \frac{1}{4} and -1 to get -\frac{1}{4}.

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

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

$$\frac{1}{3}x-1=\frac{1}{4}x-\frac{1}{4}-\frac{8}{4}$$

Since -\frac{1}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}x-1=\frac{1}{4}x+\frac{-1-8}{4}$$

Subtract 8 from -1 to get -9.

$$\frac{1}{3}x-1=\frac{1}{4}x-\frac{9}{4}$$

Subtract \frac{1}{4}x from both sides.

$$\frac{1}{3}x-1-\frac{1}{4}x=-\frac{9}{4}$$

Combine \frac{1}{3}x and -\frac{1}{4}x to get \frac{1}{12}x.

$$\frac{1}{12}x-1=-\frac{9}{4}$$

Add 1 to both sides.

$$\frac{1}{12}x=-\frac{9}{4}+1$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{1}{12}x=-\frac{9}{4}+\frac{4}{4}$$

Since -\frac{9}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\frac{1}{12}x=\frac{-9+4}{4}$$

Add -9 and 4 to get -5.

$$\frac{1}{12}x=-\frac{5}{4}$$

Multiply both sides by 12, the reciprocal of \frac{1}{12}.

$$x=-\frac{5}{4}\times 12$$

Express -\frac{5}{4}\times 12 as a single fraction.

$$x=\frac{-5\times 12}{4}$$

Multiply -5 and 12 to get -60.

$$x=\frac{-60}{4}$$

Divide -60 by 4 to get -15.

$$x=-15$$