Solve 13/4x-22/3=11/3x-1/6

$$1 \frac { 3 } { 4 } x - 2 \frac { 2 } { 3 } = 1 \frac { 1 } { 3 } x - \frac { 1 } { 6 }$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,3,6.

$$3\left(1\times 4+3\right)x-4\left(2\times 3+2\right)=4\left(1\times 3+1\right)x-2$$

Multiply 1 and 4 to get 4.

$$3\left(4+3\right)x-4\left(2\times 3+2\right)=4\left(1\times 3+1\right)x-2$$

Add 4 and 3 to get 7.

$$3\times 7x-4\left(2\times 3+2\right)=4\left(1\times 3+1\right)x-2$$

Multiply 3 and 7 to get 21.

$$21x-4\left(2\times 3+2\right)=4\left(1\times 3+1\right)x-2$$

Multiply 2 and 3 to get 6.

$$21x-4\left(6+2\right)=4\left(1\times 3+1\right)x-2$$

Add 6 and 2 to get 8.

$$21x-4\times 8=4\left(1\times 3+1\right)x-2$$

Multiply -4 and 8 to get -32.

$$21x-32=4\left(1\times 3+1\right)x-2$$

Multiply 1 and 3 to get 3.

$$21x-32=4\left(3+1\right)x-2$$

Add 3 and 1 to get 4.

$$21x-32=4\times 4x-2$$

Multiply 4 and 4 to get 16.

$$21x-32=16x-2$$

Subtract 16x from both sides.

$$21x-32-16x=-2$$

Combine 21x and -16x to get 5x.

$$5x-32=-2$$

Add 32 to both sides.

$$5x=-2+32$$

Add -2 and 32 to get 30.

$$5x=30$$

Divide both sides by 5.

$$x=\frac{30}{5}$$

Divide 30 by 5 to get 6.

$$x=6$$