Solve 1/3(x-1)+2=x+5

$$\frac{ 1 }{ 3 } (x-1)+2=x+5$$

Solve for x

$$x=-5$$

Steps for Solving Linear Equation

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

$$\frac{1}{3}x+\frac{1}{3}\left(-1\right)+2=x+5$$

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

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

Convert 2 to fraction \frac{6}{3}.

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

Since -\frac{1}{3} and \frac{6}{3} have the same denominator, add them by adding their numerators.

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

Add -1 and 6 to get 5.

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

Subtract x from both sides.

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

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

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

Subtract \frac{5}{3} from both sides.

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

Convert 5 to fraction \frac{15}{3}.

$$-\frac{2}{3}x=\frac{15}{3}-\frac{5}{3}$$

Since \frac{15}{3} and \frac{5}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{3}x=\frac{15-5}{3}$$

Subtract 5 from 15 to get 10.

$$-\frac{2}{3}x=\frac{10}{3}$$

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

$$x=\frac{10}{3}\left(-\frac{3}{2}\right)$$

Multiply \frac{10}{3} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{10\left(-3\right)}{3\times 2}$$

Do the multiplications in the fraction \frac{10\left(-3\right)}{3\times 2}.

$$x=\frac{-30}{6}$$

Divide -30 by 6 to get -5.

$$x=-5$$