Solve 21/3x-31/2x=31/5x-42/3x-9

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

Solve for x

$$x=-30$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 3,2,5.

$$10\left(2\times 3+1\right)x-15\left(3\times 2+1\right)x=30\left(\frac{3\times 5+1}{5}x-\frac{4\times 3+2}{3}x\right)-270$$

Multiply 2 and 3 to get 6.

$$10\left(6+1\right)x-15\left(3\times 2+1\right)x=30\left(\frac{3\times 5+1}{5}x-\frac{4\times 3+2}{3}x\right)-270$$

Add 6 and 1 to get 7.

$$10\times 7x-15\left(3\times 2+1\right)x=30\left(\frac{3\times 5+1}{5}x-\frac{4\times 3+2}{3}x\right)-270$$

Multiply 10 and 7 to get 70.

$$70x-15\left(3\times 2+1\right)x=30\left(\frac{3\times 5+1}{5}x-\frac{4\times 3+2}{3}x\right)-270$$

Multiply 3 and 2 to get 6.

$$70x-15\left(6+1\right)x=30\left(\frac{3\times 5+1}{5}x-\frac{4\times 3+2}{3}x\right)-270$$

Add 6 and 1 to get 7.

$$70x-15\times 7x=30\left(\frac{3\times 5+1}{5}x-\frac{4\times 3+2}{3}x\right)-270$$

Multiply 15 and 7 to get 105.

$$70x-105x=30\left(\frac{3\times 5+1}{5}x-\frac{4\times 3+2}{3}x\right)-270$$

Combine 70x and -105x to get -35x.

$$-35x=30\left(\frac{3\times 5+1}{5}x-\frac{4\times 3+2}{3}x\right)-270$$

Multiply 3 and 5 to get 15.

$$-35x=30\left(\frac{15+1}{5}x-\frac{4\times 3+2}{3}x\right)-270$$

Add 15 and 1 to get 16.

$$-35x=30\left(\frac{16}{5}x-\frac{4\times 3+2}{3}x\right)-270$$

Multiply 4 and 3 to get 12.

$$-35x=30\left(\frac{16}{5}x-\frac{12+2}{3}x\right)-270$$

Add 12 and 2 to get 14.

$$-35x=30\left(\frac{16}{5}x-\frac{14}{3}x\right)-270$$

Combine \frac{16}{5}x and -\frac{14}{3}x to get -\frac{22}{15}x.

$$-35x=30\left(-\frac{22}{15}\right)x-270$$

Express 30\left(-\frac{22}{15}\right) as a single fraction.

$$-35x=\frac{30\left(-22\right)}{15}x-270$$

Multiply 30 and -22 to get -660.

$$-35x=\frac{-660}{15}x-270$$

Divide -660 by 15 to get -44.

$$-35x=-44x-270$$

Add 44x to both sides.

$$-35x+44x=-270$$

Combine -35x and 44x to get 9x.

$$9x=-270$$

Divide both sides by 9.

$$x=\frac{-270}{9}$$

Divide -270 by 9 to get -30.

$$x=-30$$