Solve 2/3x+1+2=2/3

$$\frac { 2 } { 3 x + 1 } + 2 = \frac { 2 } { 3 }$$

Solve for x

$$x=-\frac{5}{6}\approx -0.833333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{1}{3} since division by zero is not defined. Multiply both sides of the equation by 3\left(3x+1\right), the least common multiple of 3x+1,3.

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

Multiply 3 and 2 to get 6.

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

Multiply 3 and 2 to get 6.

$$6+6\left(3x+1\right)=2\left(3x+1\right)$$

Use the distributive property to multiply 6 by 3x+1.

$$6+18x+6=2\left(3x+1\right)$$

Add 6 and 6 to get 12.

$$12+18x=2\left(3x+1\right)$$

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

$$12+18x=6x+2$$

Subtract 6x from both sides.

$$12+18x-6x=2$$

Combine 18x and -6x to get 12x.

$$12+12x=2$$

Subtract 12 from both sides.

$$12x=2-12$$

Subtract 12 from 2 to get -10.

$$12x=-10$$

Divide both sides by 12.

$$x=\frac{-10}{12}$$

Reduce the fraction \frac{-10}{12} to lowest terms by extracting and canceling out 2.

$$x=-\frac{5}{6}$$