Solve for k 5/6k+2/3=4/3

$\frac{5}{6} k + \frac{2}{3} = \frac{4}{3}$

Step 1

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

$\frac{5 k}{6} + \frac{2}{3} = \frac{4}{3}$

Step 2

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

Subtract $\frac{2}{3}$ from both sides of the equation.

$\frac{5 k}{6} = \frac{4}{3} - \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{5 k}{6} = \frac{4 - 2}{3}$

Subtract $2$ from $4$ .

$\frac{5 k}{6} = \frac{2}{3}$

Step 3

Multiply both sides of the equation by $\frac{6}{5}$ .

$\frac{6}{5} \cdot \frac{5 k}{6} = \frac{6}{5} \cdot \frac{2}{3}$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{6}{5} \cdot \frac{5 k}{6}$ .

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6}{5} \cdot \frac{5 k}{6} = \frac{6}{5} \cdot \frac{2}{3}$

Rewrite the expression.

$\frac{1}{5} (5 k) = \frac{6}{5} \cdot \frac{2}{3}$

Cancel the common factor of $5$ .

Factor $5$ out of $5 k$ .

$\frac{1}{5} (5 (k)) = \frac{6}{5} \cdot \frac{2}{3}$

Cancel the common factor.

$\frac{1}{5} (5 k) = \frac{6}{5} \cdot \frac{2}{3}$

Rewrite the expression.

$k = \frac{6}{5} \cdot \frac{2}{3}$

Simplify the right side.

Simplify $\frac{6}{5} \cdot \frac{2}{3}$ .

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$k = \frac{3 (2)}{5} \cdot \frac{2}{3}$

Cancel the common factor.

$k = \frac{3 \cdot 2}{5} \cdot \frac{2}{3}$

Rewrite the expression.

$k = \frac{2}{5} \cdot 2$

Combine $\frac{2}{5}$ and $2$ .

$k = \frac{2 \cdot 2}{5}$

Multiply $2$ by $2$ .

$k = \frac{4}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$k = \frac{4}{5}$

Decimal Form:

$k = 0.8$

Solve for k 5/6k+2/3=4/3

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