Solve 3x+1/3-21/6=5x+8/3

$$\frac { 3 x + 1 } { 3 } - 2 \frac { 1 } { 6 } = \frac { 5 x + 8 } { 3 }$$

Solve for x

$$x = -\frac{27}{4} = -6\frac{3}{4} = -6.75$$

Steps for Solving Linear Equation

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

$$2\left(3x+1\right)-\left(2\times 6+1\right)=2\left(5x+8\right)$$

Use the distributive property to multiply 2 by 3x+1.

$$6x+2-\left(2\times 6+1\right)=2\left(5x+8\right)$$

Multiply 2 and 6 to get 12.

$$6x+2-\left(12+1\right)=2\left(5x+8\right)$$

Add 12 and 1 to get 13.

$$6x+2-13=2\left(5x+8\right)$$

Subtract 13 from 2 to get -11.

$$6x-11=2\left(5x+8\right)$$

Use the distributive property to multiply 2 by 5x+8.

$$6x-11=10x+16$$

Subtract 10x from both sides.

$$6x-11-10x=16$$

Combine 6x and -10x to get -4x.

$$-4x-11=16$$

Add 11 to both sides.

$$-4x=16+11$$

Add 16 and 11 to get 27.

$$-4x=27$$

Divide both sides by -4.

$$x=\frac{27}{-4}$$

Fraction \frac{27}{-4} can be rewritten as -\frac{27}{4} by extracting the negative sign.

$$x=-\frac{27}{4}$$