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

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

Solve for x

$$x = -\frac{9}{7} = -1\frac{2}{7} \approx -1.285714286$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 21, the least common multiple of 3,7.

$$7\times 2\left(x-3\right)-63x=6+7\times 3\left(x+2\right)$$

Multiply 7 and 2 to get 14.

$$14\left(x-3\right)-63x=6+7\times 3\left(x+2\right)$$

Use the distributive property to multiply 14 by x-3.

$$14x-42-63x=6+7\times 3\left(x+2\right)$$

Combine 14x and -63x to get -49x.

$$-49x-42=6+7\times 3\left(x+2\right)$$

Multiply 7 and 3 to get 21.

$$-49x-42=6+21\left(x+2\right)$$

Use the distributive property to multiply 21 by x+2.

$$-49x-42=6+21x+42$$

Add 6 and 42 to get 48.

$$-49x-42=48+21x$$

Subtract 21x from both sides.

$$-49x-42-21x=48$$

Combine -49x and -21x to get -70x.

$$-70x-42=48$$

Add 42 to both sides.

$$-70x=48+42$$

Add 48 and 42 to get 90.

$$-70x=90$$

Divide both sides by -70.

$$x=\frac{90}{-70}$$

Reduce the fraction \frac{90}{-70} to lowest terms by extracting and canceling out 10.

$$x=-\frac{9}{7}$$