Solve for x 1/3x+4=x-2

$\frac{1}{3} x + 4 = x - 2$

Step 1

Combine $\frac{1}{3}$ and $x$ .

$\frac{x}{3} + 4 = x - 2$

Step 2

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$\frac{x}{3} + 4 - x = - 2$

To write $- x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{3} - x \cdot \frac{3}{3} + 4 = - 2$

Combine $- x$ and $\frac{3}{3}$ .

$\frac{x}{3} + \frac{- x \cdot 3}{3} + 4 = - 2$

Combine the numerators over the common denominator.

$\frac{x - x \cdot 3}{3} + 4 = - 2$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $x - x \cdot 3$ .

Raise $x$ to the power of $1$ .

$\frac{x^{1} - x \cdot 3}{3} + 4 = - 2$

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1 - x \cdot 3}{3} + 4 = - 2$

Factor $x$ out of $- x \cdot 3$ .

$\frac{x \cdot 1 + x (- 1 \cdot 3)}{3} + 4 = - 2$

Factor $x$ out of $x \cdot 1 + x (- 1 \cdot 3)$ .

$\frac{x (1 - 1 \cdot 3)}{3} + 4 = - 2$

Multiply $- 1$ by $3$ .

$\frac{x (1 - 3)}{3} + 4 = - 2$

Subtract $3$ from $1$ .

$\frac{x \cdot - 2}{3} + 4 = - 2$

Move $- 2$ to the left of $x$ .

$\frac{- 2 \cdot x}{3} + 4 = - 2$

Move the negative in front of the fraction.

$- \frac{2 x}{3} + 4 = - 2$

Step 3

Move all terms not containing $x$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$- \frac{2 x}{3} = - 2 - 4$

Subtract $4$ from $- 2$ .

$- \frac{2 x}{3} = - 6$

Step 4

Multiply both sides of the equation by $- \frac{3}{2}$ .

$- \frac{3}{2} (- \frac{2 x}{3}) = - \frac{3}{2} \cdot - 6$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{2} (- \frac{2 x}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$\frac{- 3}{2} (- \frac{2 x}{3}) = - \frac{3}{2} \cdot - 6$

Move the leading negative in $- \frac{2 x}{3}$ into the numerator.

$\frac{- 3}{2} \cdot \frac{- 2 x}{3} = - \frac{3}{2} \cdot - 6$

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{2} \cdot \frac{- 2 x}{3} = - \frac{3}{2} \cdot - 6$

Cancel the common factor.

$\frac{3 \cdot - 1}{2} \cdot \frac{- 2 x}{3} = - \frac{3}{2} \cdot - 6$

Rewrite the expression.

$\frac{- 1}{2} (- 2 x) = - \frac{3}{2} \cdot - 6$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 x$ .

$\frac{- 1}{2} (2 (- x)) = - \frac{3}{2} \cdot - 6$

Cancel the common factor.

$\frac{- 1}{2} (2 (- x)) = - \frac{3}{2} \cdot - 6$

Rewrite the expression.

$- - x = - \frac{3}{2} \cdot - 6$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{3}{2} \cdot - 6$

Multiply $x$ by $1$ .

$x = - \frac{3}{2} \cdot - 6$

Simplify the right side.

Simplify $- \frac{3}{2} \cdot - 6$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$x = \frac{- 3}{2} \cdot - 6$

Factor $2$ out of $- 6$ .

$x = \frac{- 3}{2} \cdot (2 (- 3))$

Cancel the common factor.

$x = \frac{- 3}{2} \cdot (2 \cdot - 3)$

Rewrite the expression.

$x = - 3 \cdot - 3$

Multiply $- 3$ by $- 3$ .

$x = 9$

Solve for x 1/3x+4=x-2

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