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

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

Step 1

Combine $\frac{4}{3}$ and $x$ .

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

Step 2

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

Subtract $x$ from both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $4 x - x \cdot 3$ .

Factor $x$ out of $4 x$ .

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

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

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

Factor $x$ out of $x \cdot 4 + x (- 1 \cdot 3)$ .

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

Multiply $- 1$ by $3$ .

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

Subtract $3$ from $4$ .

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

Multiply $x$ by $1$ .

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

Step 3

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

Subtract $2$ from both sides of the equation.

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

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Combine $- 2$ and $\frac{3}{3}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 2$ by $3$ .

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

Subtract $6$ from $- 1$ .

$\frac{x}{3} = \frac{- 7}{3}$

Move the negative in front of the fraction.

$\frac{x}{3} = - \frac{7}{3}$

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x = - 7$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.