Solve 5x/3-x-2/4=9/4-1/2(x-frac{2x-1}{3})

$$\frac{ 5x }{ 3 } - \frac{ x-2 }{ 4 } = \frac{ 9 }{ 4 } - \frac{ 1 }{ 2 } (x- \frac{ 2x-1 }{ 3 } )$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

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

$$4\times 5x-3\left(x-2\right)=27-6\left(x-\frac{2x-1}{3}\right)$$

Multiply 4 and 5 to get 20.

$$20x-3\left(x-2\right)=27-6\left(x-\frac{2x-1}{3}\right)$$

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

$$20x-3x+6=27-6\left(x-\frac{2x-1}{3}\right)$$

Combine 20x and -3x to get 17x.

$$17x+6=27-6\left(x-\frac{2x-1}{3}\right)$$

Divide each term of 2x-1 by 3 to get \frac{2}{3}x-\frac{1}{3}.

$$17x+6=27-6\left(x-\left(\frac{2}{3}x-\frac{1}{3}\right)\right)$$

To find the opposite of \frac{2}{3}x-\frac{1}{3}, find the opposite of each term.

$$17x+6=27-6\left(x-\frac{2}{3}x-\left(-\frac{1}{3}\right)\right)$$

The opposite of -\frac{1}{3} is \frac{1}{3}.

$$17x+6=27-6\left(x-\frac{2}{3}x+\frac{1}{3}\right)$$

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

$$17x+6=27-6\left(\frac{1}{3}x+\frac{1}{3}\right)$$

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

$$17x+6=27-6\times \frac{1}{3}x-6\times \frac{1}{3}$$

Multiply -6 and \frac{1}{3} to get \frac{-6}{3}.

$$17x+6=27+\frac{-6}{3}x-6\times \frac{1}{3}$$

Divide -6 by 3 to get -2.

$$17x+6=27-2x-6\times \frac{1}{3}$$

Multiply -6 and \frac{1}{3} to get \frac{-6}{3}.

$$17x+6=27-2x+\frac{-6}{3}$$

Divide -6 by 3 to get -2.

$$17x+6=27-2x-2$$

Subtract 2 from 27 to get 25.

$$17x+6=25-2x$$

Add 2x to both sides.

$$17x+6+2x=25$$

Combine 17x and 2x to get 19x.

$$19x+6=25$$

Subtract 6 from both sides.

$$19x=25-6$$

Subtract 6 from 25 to get 19.

$$19x=19$$

Divide both sides by 19.

$$x=\frac{19}{19}$$

Divide 19 by 19 to get 1.

$$x=1$$