Solve 1/3(2x-1/2)-3/2(1/4-frac{x}{6})=2(frac{1}{6}x-frac{1}{3})

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

Solve for x

$$x=-\frac{3}{14}\approx -0.214285714$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,2,4,6.

$$4\left(2x-\frac{1}{2}\right)-18\left(\frac{1}{4}-\frac{x}{6}\right)=24\left(\frac{1}{6}x-\frac{1}{3}\right)$$

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

$$8x+4\left(-\frac{1}{2}\right)-18\left(\frac{1}{4}-\frac{x}{6}\right)=24\left(\frac{1}{6}x-\frac{1}{3}\right)$$

Express 4\left(-\frac{1}{2}\right) as a single fraction.

$$8x+\frac{4\left(-1\right)}{2}-18\left(\frac{1}{4}-\frac{x}{6}\right)=24\left(\frac{1}{6}x-\frac{1}{3}\right)$$

Multiply 4 and -1 to get -4.

$$8x+\frac{-4}{2}-18\left(\frac{1}{4}-\frac{x}{6}\right)=24\left(\frac{1}{6}x-\frac{1}{3}\right)$$

Divide -4 by 2 to get -2.

$$8x-2-18\left(\frac{1}{4}-\frac{x}{6}\right)=24\left(\frac{1}{6}x-\frac{1}{3}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 6 is 12. Multiply \frac{1}{4} times \frac{3}{3}. Multiply \frac{x}{6} times \frac{2}{2}.

$$8x-2-18\left(\frac{3}{12}-\frac{2x}{12}\right)=24\left(\frac{1}{6}x-\frac{1}{3}\right)$$

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

$$8x-2-18\times \frac{3-2x}{12}=24\left(\frac{1}{6}x-\frac{1}{3}\right)$$

Express 18\times \frac{3-2x}{12} as a single fraction.

$$8x-2-\frac{18\left(3-2x\right)}{12}=24\left(\frac{1}{6}x-\frac{1}{3}\right)$$

Use the distributive property to multiply 18 by 3-2x.

$$8x-2-\frac{54-36x}{12}=24\left(\frac{1}{6}x-\frac{1}{3}\right)$$

Use the distributive property to multiply 24 by \frac{1}{6}x-\frac{1}{3}.

$$8x-2-\frac{54-36x}{12}=24\times \frac{1}{6}x+24\left(-\frac{1}{3}\right)$$

Multiply 24 and \frac{1}{6} to get \frac{24}{6}.

$$8x-2-\frac{54-36x}{12}=\frac{24}{6}x+24\left(-\frac{1}{3}\right)$$

Divide 24 by 6 to get 4.

$$8x-2-\frac{54-36x}{12}=4x+24\left(-\frac{1}{3}\right)$$

Express 24\left(-\frac{1}{3}\right) as a single fraction.

$$8x-2-\frac{54-36x}{12}=4x+\frac{24\left(-1\right)}{3}$$

Multiply 24 and -1 to get -24.

$$8x-2-\frac{54-36x}{12}=4x+\frac{-24}{3}$$

Divide -24 by 3 to get -8.

$$8x-2-\frac{54-36x}{12}=4x-8$$

Divide each term of 54-36x by 12 to get \frac{9}{2}-3x.

$$8x-2-\left(\frac{9}{2}-3x\right)=4x-8$$

To find the opposite of \frac{9}{2}-3x, find the opposite of each term.

$$8x-2-\frac{9}{2}-\left(-3x\right)=4x-8$$

The opposite of -3x is 3x.

$$8x-2-\frac{9}{2}+3x=4x-8$$

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

$$8x-\frac{4}{2}-\frac{9}{2}+3x=4x-8$$

Since -\frac{4}{2} and \frac{9}{2} have the same denominator, subtract them by subtracting their numerators.

$$8x+\frac{-4-9}{2}+3x=4x-8$$

Subtract 9 from -4 to get -13.

$$8x-\frac{13}{2}+3x=4x-8$$

Combine 8x and 3x to get 11x.

$$11x-\frac{13}{2}=4x-8$$

Subtract 4x from both sides.

$$11x-\frac{13}{2}-4x=-8$$

Combine 11x and -4x to get 7x.

$$7x-\frac{13}{2}=-8$$

Add \frac{13}{2} to both sides.

$$7x=-8+\frac{13}{2}$$

Convert -8 to fraction -\frac{16}{2}.

$$7x=-\frac{16}{2}+\frac{13}{2}$$

Since -\frac{16}{2} and \frac{13}{2} have the same denominator, add them by adding their numerators.

$$7x=\frac{-16+13}{2}$$

Add -16 and 13 to get -3.

$$7x=-\frac{3}{2}$$

Divide both sides by 7.

$$x=\frac{-\frac{3}{2}}{7}$$

Express \frac{-\frac{3}{2}}{7} as a single fraction.

$$x=\frac{-3}{2\times 7}$$

Multiply 2 and 7 to get 14.

$$x=\frac{-3}{14}$$

Fraction \frac{-3}{14} can be rewritten as -\frac{3}{14} by extracting the negative sign.

$$x=-\frac{3}{14}$$