Solve 2(x-3)/3-6(x-2)/2=7x-2/6-2x-2/2

$$\frac { 2 ( x - 3 ) } { 3 } - \frac { 6 ( x - 2 ) } { 2 } = \frac { 7 x - 2 } { 6 } - \frac { 2 x - 2 } { 2 }$$

Solve for x

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

Steps for Solving Linear Equation

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

$$2\times 2\left(x-3\right)-3\times 6\left(x-2\right)=7x-2-3\left(2x-2\right)$$

Multiply 2 and 2 to get 4.

$$4\left(x-3\right)-3\times 6\left(x-2\right)=7x-2-3\left(2x-2\right)$$

Use the distributive property to multiply 4 by x-3.

$$4x-12-3\times 6\left(x-2\right)=7x-2-3\left(2x-2\right)$$

Multiply -3 and 6 to get -18.

$$4x-12-18\left(x-2\right)=7x-2-3\left(2x-2\right)$$

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

$$4x-12-18x+36=7x-2-3\left(2x-2\right)$$

Combine 4x and -18x to get -14x.

$$-14x-12+36=7x-2-3\left(2x-2\right)$$

Add -12 and 36 to get 24.

$$-14x+24=7x-2-3\left(2x-2\right)$$

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

$$-14x+24=7x-2-6x+6$$

Combine 7x and -6x to get x.

$$-14x+24=x-2+6$$

Add -2 and 6 to get 4.

$$-14x+24=x+4$$

Subtract x from both sides.

$$-14x+24-x=4$$

Combine -14x and -x to get -15x.

$$-15x+24=4$$

Subtract 24 from both sides.

$$-15x=4-24$$

Subtract 24 from 4 to get -20.

$$-15x=-20$$

Divide both sides by -15.

$$x=\frac{-20}{-15}$$

Reduce the fraction \frac{-20}{-15} to lowest terms by extracting and canceling out -5.

$$x=\frac{4}{3}$$