Solve for x 5/3x+1/3x=13 1/3+8/3x

$\frac{5}{3} x + \frac{1}{3} x = 13 \frac{1}{3} + \frac{8}{3} x$

Step 1

Simplify the left side.

Simplify $\frac{5}{3} x + \frac{1}{3} x$ .

Simplify each term.

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

$\frac{5 x}{3} + \frac{1}{3} x = 13 \frac{1}{3} + \frac{8}{3} x$

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

$\frac{5 x}{3} + \frac{x}{3} = 13 \frac{1}{3} + \frac{8}{3} x$

Simplify terms.

Combine the numerators over the common denominator.

$\frac{5 x + x}{3} = 13 \frac{1}{3} + \frac{8}{3} x$

Add $5 x$ and $x$ .

$\frac{6 x}{3} = 13 \frac{1}{3} + \frac{8}{3} x$

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6 x$ .

$\frac{3 (2 x)}{3} = 13 \frac{1}{3} + \frac{8}{3} x$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (2 x)}{3 (1)} = 13 \frac{1}{3} + \frac{8}{3} x$

Cancel the common factor.

$\frac{3 (2 x)}{3 \cdot 1} = 13 \frac{1}{3} + \frac{8}{3} x$

Rewrite the expression.

$\frac{2 x}{1} = 13 \frac{1}{3} + \frac{8}{3} x$

Divide $2 x$ by $1$ .

$2 x = 13 \frac{1}{3} + \frac{8}{3} x$

Step 2

Simplify the right side.

Simplify $13 \frac{1}{3} + \frac{8}{3} x$ .

Convert $13 \frac{1}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$2 x = 13 + \frac{1}{3} + \frac{8}{3} x$

Add $13$ and $\frac{1}{3}$ .

To write $13$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$2 x = 13 \cdot \frac{3}{3} + \frac{1}{3} + \frac{8}{3} x$

Combine $13$ and $\frac{3}{3}$ .

$2 x = \frac{13 \cdot 3}{3} + \frac{1}{3} + \frac{8}{3} x$

Combine the numerators over the common denominator.

$2 x = \frac{13 \cdot 3 + 1}{3} + \frac{8}{3} x$

Simplify the numerator.

Multiply $13$ by $3$ .

$2 x = \frac{39 + 1}{3} + \frac{8}{3} x$

Add $39$ and $1$ .

$2 x = \frac{40}{3} + \frac{8}{3} x$

Combine $\frac{8}{3}$ and $x$ .

$2 x = \frac{40}{3} + \frac{8 x}{3}$

Step 3

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

Subtract $\frac{8 x}{3}$ from both sides of the equation.

$2 x - \frac{8 x}{3} = \frac{40}{3}$

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

$2 x \cdot \frac{3}{3} - \frac{8 x}{3} = \frac{40}{3}$

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

$\frac{2 x \cdot 3}{3} - \frac{8 x}{3} = \frac{40}{3}$

Combine the numerators over the common denominator.

$\frac{2 x \cdot 3 - 8 x}{3} = \frac{40}{3}$

Simplify the numerator.

Factor $2 x$ out of $2 x \cdot 3 - 8 x$ .

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

$\frac{2 x (3) - 8 x}{3} = \frac{40}{3}$

Factor $2 x$ out of $- 8 x$ .

$\frac{2 x (3) + 2 x (- 4)}{3} = \frac{40}{3}$

Factor $2 x$ out of $2 x (3) + 2 x (- 4)$ .

$\frac{2 x (3 - 4)}{3} = \frac{40}{3}$

Subtract $4$ from $3$ .

$\frac{2 x \cdot - 1}{3} = \frac{40}{3}$

Multiply $- 1$ by $2$ .

$\frac{- 2 x}{3} = \frac{40}{3}$

Move the negative in front of the fraction.

$- \frac{2 x}{3} = \frac{40}{3}$

Step 4

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

$- 2 x = 40$

Step 5

Divide each term in $- 2 x = 40$ by $- 2$ and simplify.

Divide each term in $- 2 x = 40$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{40}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{40}{- 2}$

Divide $x$ by $1$ .

$x = \frac{40}{- 2}$

Simplify the right side.

Divide $40$ by $- 2$ .

$x = - 20$

Solve for x 5/3x+1/3x=13 1/3+8/3x

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