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

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

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by 2+x.

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

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

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

Convert 1 to fraction \frac{3}{3}.

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

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

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

Add 2 and 3 to get 5.

$$\frac{5}{3}+\frac{1}{3}x=x$$

Subtract x from both sides.

$$\frac{5}{3}+\frac{1}{3}x-x=0$$

Combine \frac{1}{3}x and -x to get -\frac{2}{3}x.

$$\frac{5}{3}-\frac{2}{3}x=0$$

Subtract \frac{5}{3} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{2}{3}x=-\frac{5}{3}$$

Multiply both sides by -\frac{3}{2}, the reciprocal of -\frac{2}{3}.

$$x=-\frac{5}{3}\left(-\frac{3}{2}\right)$$

Multiply -\frac{5}{3} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-5\left(-3\right)}{3\times 2}$$

Do the multiplications in the fraction \frac{-5\left(-3\right)}{3\times 2}.

$$x=\frac{15}{6}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$x=\frac{5}{2}$$