Solve for x 2/3x+4=5x-1/3

$\frac{2}{3} x + 4 = 5 x - \frac{1}{3}$

Step 1

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

$\frac{2 x}{3} + 4 = 5 x - \frac{1}{3}$

Step 2

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

Subtract $5 x$ from both sides of the equation.

$\frac{2 x}{3} + 4 - 5 x = - \frac{1}{3}$

To write $- 5 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 x}{3} - 5 x \cdot \frac{3}{3} + 4 = - \frac{1}{3}$

Combine $- 5 x$ and $\frac{3}{3}$ .

$\frac{2 x}{3} + \frac{- 5 x \cdot 3}{3} + 4 = - \frac{1}{3}$

Combine the numerators over the common denominator.

$\frac{2 x - 5 x \cdot 3}{3} + 4 = - \frac{1}{3}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $2 x - 5 x \cdot 3$ .

Factor $x$ out of $2 x$ .

$\frac{x \cdot 2 - 5 x \cdot 3}{3} + 4 = - \frac{1}{3}$

Factor $x$ out of $- 5 x \cdot 3$ .

$\frac{x \cdot 2 + x (- 5 \cdot 3)}{3} + 4 = - \frac{1}{3}$

Factor $x$ out of $x \cdot 2 + x (- 5 \cdot 3)$ .

$\frac{x (2 - 5 \cdot 3)}{3} + 4 = - \frac{1}{3}$

Multiply $- 5$ by $3$ .

$\frac{x (2 - 15)}{3} + 4 = - \frac{1}{3}$

Subtract $15$ from $2$ .

$\frac{x \cdot - 13}{3} + 4 = - \frac{1}{3}$

Move $- 13$ to the left of $x$ .

$\frac{- 13 \cdot x}{3} + 4 = - \frac{1}{3}$

Move the negative in front of the fraction.

$- \frac{13 x}{3} + 4 = - \frac{1}{3}$

Step 3

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

Subtract $4$ from both sides of the equation.

$- \frac{13 x}{3} = - \frac{1}{3} - 4$

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{13 x}{3} = - \frac{1}{3} - 4 \cdot \frac{3}{3}$

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

$- \frac{13 x}{3} = - \frac{1}{3} + \frac{- 4 \cdot 3}{3}$

Combine the numerators over the common denominator.

$- \frac{13 x}{3} = \frac{- 1 - 4 \cdot 3}{3}$

Simplify the numerator.

Multiply $- 4$ by $3$ .

$- \frac{13 x}{3} = \frac{- 1 - 12}{3}$

Subtract $12$ from $- 1$ .

$- \frac{13 x}{3} = \frac{- 13}{3}$

Move the negative in front of the fraction.

$- \frac{13 x}{3} = - \frac{13}{3}$

Step 4

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

$- 13 x = - 13$

Step 5

Divide each term in $- 13 x = - 13$ by $- 13$ and simplify.

Divide each term in $- 13 x = - 13$ by $- 13$ .

$\frac{- 13 x}{- 13} = \frac{- 13}{- 13}$

Simplify the left side.

Cancel the common factor of $- 13$ .

Cancel the common factor.

$\frac{- 13 x}{- 13} = \frac{- 13}{- 13}$

Divide $x$ by $1$ .

$x = \frac{- 13}{- 13}$

Simplify the right side.

Divide $- 13$ by $- 13$ .

$x = 1$

Solve for x 2/3x+4=5x-1/3

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