Solve 3/5(x-1/3+1)+x=3/4(x-2/3)

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

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 5,3,4.

$$36\left(\frac{x-1}{3}+1\right)+60x=45\left(x-\frac{2}{3}\right)$$

Use the distributive property to multiply 36 by \frac{x-1}{3}+1.

$$36\times \frac{x-1}{3}+36+60x=45\left(x-\frac{2}{3}\right)$$

Cancel out 3, the greatest common factor in 36 and 3.

$$12\left(x-1\right)+36+60x=45\left(x-\frac{2}{3}\right)$$

Use the distributive property to multiply 12 by x-1.

$$12x-12+36+60x=45\left(x-\frac{2}{3}\right)$$

Add -12 and 36 to get 24.

$$12x+24+60x=45\left(x-\frac{2}{3}\right)$$

Combine 12x and 60x to get 72x.

$$72x+24=45\left(x-\frac{2}{3}\right)$$

Use the distributive property to multiply 45 by x-\frac{2}{3}.

$$72x+24=45x+45\left(-\frac{2}{3}\right)$$

Express 45\left(-\frac{2}{3}\right) as a single fraction.

$$72x+24=45x+\frac{45\left(-2\right)}{3}$$

Multiply 45 and -2 to get -90.

$$72x+24=45x+\frac{-90}{3}$$

Divide -90 by 3 to get -30.

$$72x+24=45x-30$$

Subtract 45x from both sides.

$$72x+24-45x=-30$$

Combine 72x and -45x to get 27x.

$$27x+24=-30$$

Subtract 24 from both sides.

$$27x=-30-24$$

Subtract 24 from -30 to get -54.

$$27x=-54$$

Divide both sides by 27.

$$x=\frac{-54}{27}$$

Divide -54 by 27 to get -2.

$$x=-2$$