Solve 2/3+1/3(x+1)>0

$$\frac{ 2 }{ 3 } + \frac{ 1 }{ 3 } (x+1) > 0$$

Solve for x

$$x>-3$$

Solution Steps

Use the distributive property to multiply \frac{1}{3} by x+1.

$$\frac{2}{3}+\frac{1}{3}x+\frac{1}{3}>0$$

Since \frac{2}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{2+1}{3}+\frac{1}{3}x>0$$

Add 2 and 1 to get 3.

$$\frac{3}{3}+\frac{1}{3}x>0$$

Divide 3 by 3 to get 1.

$$1+\frac{1}{3}x>0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$\frac{1}{3}x>-1$$

Multiply both sides by 3, the reciprocal of \frac{1}{3}. Since \frac{1}{3} is positive, the inequality direction remains the same.

$$x>-3$$