Solve 1/2*(4x-1)-1/9*(3x-6)=1/4*(6x-1)

$$\frac { 1 } { 2 } \cdot ( 4 x - 1 ) - \frac { 1 } { 9 } \cdot ( 3 x - 6 ) = \frac { 1 } { 4 } \cdot ( 6 x - 1 )$$

Solve for x

$$x = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by 4x-1.

$$\frac{1}{2}\times 4x+\frac{1}{2}\left(-1\right)-\frac{1}{9}\left(3x-6\right)=\frac{1}{4}\left(6x-1\right)$$

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$\frac{4}{2}x+\frac{1}{2}\left(-1\right)-\frac{1}{9}\left(3x-6\right)=\frac{1}{4}\left(6x-1\right)$$

Divide 4 by 2 to get 2.

$$2x+\frac{1}{2}\left(-1\right)-\frac{1}{9}\left(3x-6\right)=\frac{1}{4}\left(6x-1\right)$$

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

$$2x-\frac{1}{2}-\frac{1}{9}\left(3x-6\right)=\frac{1}{4}\left(6x-1\right)$$

Use the distributive property to multiply -\frac{1}{9} by 3x-6.

$$2x-\frac{1}{2}-\frac{1}{9}\times 3x-\frac{1}{9}\left(-6\right)=\frac{1}{4}\left(6x-1\right)$$

Express -\frac{1}{9}\times 3 as a single fraction.

$$2x-\frac{1}{2}+\frac{-3}{9}x-\frac{1}{9}\left(-6\right)=\frac{1}{4}\left(6x-1\right)$$

Reduce the fraction \frac{-3}{9} to lowest terms by extracting and canceling out 3.

$$2x-\frac{1}{2}-\frac{1}{3}x-\frac{1}{9}\left(-6\right)=\frac{1}{4}\left(6x-1\right)$$

Express -\frac{1}{9}\left(-6\right) as a single fraction.

$$2x-\frac{1}{2}-\frac{1}{3}x+\frac{-\left(-6\right)}{9}=\frac{1}{4}\left(6x-1\right)$$

Multiply -1 and -6 to get 6.

$$2x-\frac{1}{2}-\frac{1}{3}x+\frac{6}{9}=\frac{1}{4}\left(6x-1\right)$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$2x-\frac{1}{2}-\frac{1}{3}x+\frac{2}{3}=\frac{1}{4}\left(6x-1\right)$$

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

$$\frac{5}{3}x-\frac{1}{2}+\frac{2}{3}=\frac{1}{4}\left(6x-1\right)$$

Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{5}{3}x-\frac{3}{6}+\frac{4}{6}=\frac{1}{4}\left(6x-1\right)$$

Since -\frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{5}{3}x+\frac{-3+4}{6}=\frac{1}{4}\left(6x-1\right)$$

Add -3 and 4 to get 1.

$$\frac{5}{3}x+\frac{1}{6}=\frac{1}{4}\left(6x-1\right)$$

Use the distributive property to multiply \frac{1}{4} by 6x-1.

$$\frac{5}{3}x+\frac{1}{6}=\frac{1}{4}\times 6x+\frac{1}{4}\left(-1\right)$$

Multiply \frac{1}{4} and 6 to get \frac{6}{4}.

$$\frac{5}{3}x+\frac{1}{6}=\frac{6}{4}x+\frac{1}{4}\left(-1\right)$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{5}{3}x+\frac{1}{6}=\frac{3}{2}x+\frac{1}{4}\left(-1\right)$$

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

$$\frac{5}{3}x+\frac{1}{6}=\frac{3}{2}x-\frac{1}{4}$$

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

$$\frac{5}{3}x+\frac{1}{6}-\frac{3}{2}x=-\frac{1}{4}$$

Combine \frac{5}{3}x and -\frac{3}{2}x to get \frac{1}{6}x.

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

Subtract \frac{1}{6} from both sides.

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

Least common multiple of 4 and 6 is 12. Convert -\frac{1}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{1}{6}x=-\frac{3}{12}-\frac{2}{12}$$

Since -\frac{3}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{6}x=\frac{-3-2}{12}$$

Subtract 2 from -3 to get -5.

$$\frac{1}{6}x=-\frac{5}{12}$$

Multiply both sides by 6, the reciprocal of \frac{1}{6}.

$$x=-\frac{5}{12}\times 6$$

Express -\frac{5}{12}\times 6 as a single fraction.

$$x=\frac{-5\times 6}{12}$$

Multiply -5 and 6 to get -30.

$$x=\frac{-30}{12}$$

Reduce the fraction \frac{-30}{12} to lowest terms by extracting and canceling out 6.

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