Solve for x 5/6x-3x+8/3=5/3

$\frac{5}{6} x - 3 x + \frac{8}{3} = \frac{5}{3}$

Step 1

Simplify $\frac{5}{6} x - 3 x + \frac{8}{3}$ .

Combine $\frac{5}{6}$ and $x$ .

$\frac{5 x}{6} - 3 x + \frac{8}{3} = \frac{5}{3}$

To write $- 3 x$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{5 x}{6} - 3 x \cdot \frac{6}{6} + \frac{8}{3} = \frac{5}{3}$

Simplify terms.

Combine $- 3 x$ and $\frac{6}{6}$ .

$\frac{5 x}{6} + \frac{- 3 x \cdot 6}{6} + \frac{8}{3} = \frac{5}{3}$

Combine the numerators over the common denominator.

$\frac{5 x - 3 x \cdot 6}{6} + \frac{8}{3} = \frac{5}{3}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $5 x - 3 x \cdot 6$ .

Factor $x$ out of $5 x$ .

$\frac{x \cdot 5 - 3 x \cdot 6}{6} + \frac{8}{3} = \frac{5}{3}$

Factor $x$ out of $- 3 x \cdot 6$ .

$\frac{x \cdot 5 + x (- 3 \cdot 6)}{6} + \frac{8}{3} = \frac{5}{3}$

Factor $x$ out of $x \cdot 5 + x (- 3 \cdot 6)$ .

$\frac{x (5 - 3 \cdot 6)}{6} + \frac{8}{3} = \frac{5}{3}$

Multiply $- 3$ by $6$ .

$\frac{x (5 - 18)}{6} + \frac{8}{3} = \frac{5}{3}$

Subtract $18$ from $5$ .

$\frac{x \cdot - 13}{6} + \frac{8}{3} = \frac{5}{3}$

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

$\frac{- 13 \cdot x}{6} + \frac{8}{3} = \frac{5}{3}$

Move the negative in front of the fraction.

$- \frac{13 x}{6} + \frac{8}{3} = \frac{5}{3}$

Step 2

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

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

$- \frac{13 x}{6} = \frac{5}{3} - \frac{8}{3}$

Combine the numerators over the common denominator.

$- \frac{13 x}{6} = \frac{5 - 8}{3}$

Subtract $8$ from $5$ .

$- \frac{13 x}{6} = \frac{- 3}{3}$

Divide $- 3$ by $3$ .

$- \frac{13 x}{6} = - 1$

Step 3

Multiply both sides of the equation by $- \frac{6}{13}$ .

$- \frac{6}{13} (- \frac{13 x}{6}) = - \frac{6}{13} \cdot - 1$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{6}{13} (- \frac{13 x}{6})$ .

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{6}{13}$ into the numerator.

$\frac{- 6}{13} (- \frac{13 x}{6}) = - \frac{6}{13} \cdot - 1$

Move the leading negative in $- \frac{13 x}{6}$ into the numerator.

$\frac{- 6}{13} \cdot \frac{- 13 x}{6} = - \frac{6}{13} \cdot - 1$

Factor $6$ out of $- 6$ .

$\frac{6 (- 1)}{13} \cdot \frac{- 13 x}{6} = - \frac{6}{13} \cdot - 1$

Cancel the common factor.

$\frac{6 \cdot - 1}{13} \cdot \frac{- 13 x}{6} = - \frac{6}{13} \cdot - 1$

Rewrite the expression.

$\frac{- 1}{13} (- 13 x) = - \frac{6}{13} \cdot - 1$

Cancel the common factor of $13$ .

Factor $13$ out of $- 13 x$ .

$\frac{- 1}{13} (13 (- x)) = - \frac{6}{13} \cdot - 1$

Cancel the common factor.

$\frac{- 1}{13} (13 (- x)) = - \frac{6}{13} \cdot - 1$

Rewrite the expression.

$- - x = - \frac{6}{13} \cdot - 1$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{6}{13} \cdot - 1$

Multiply $x$ by $1$ .

$x = - \frac{6}{13} \cdot - 1$

Simplify the right side.

Multiply $- \frac{6}{13} \cdot - 1$ .

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{6}{13})$

Multiply $\frac{6}{13}$ by $1$ .

$x = \frac{6}{13}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{6}{13}$

Decimal Form:

$x = 0.\overline{461538}$

Solve for x 5/6x-3x+8/3=5/3

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