Solve for k 1/2k-3=2-3/4k

$\frac{1}{2} k - 3 = 2 - \frac{3}{4} k$

Combine $\frac{1}{2}$ and $k$ .

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

Simplify each term.

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

$\frac{k}{2} - 3 = 2 - \frac{k \cdot 3}{4}$

Move $3$ to the left of $k$ .

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

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

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Add $\frac{3 k}{4}$ to both sides of the equation.

$\frac{k}{2} - 3 + \frac{3 k}{4} = 2$

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

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

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{k}{2}$ and $\frac{2}{2}$ .

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

Multiply $2$ by $2$ .

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

Combine the numerators over the common denominator.

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

Add $k \cdot 2$ and $3 k$ .

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Reorder $k$ and $2$ .

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

Add $2 \cdot k$ and $3 k$ .

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

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

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

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Add $3$ to both sides of the equation.

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

Add $2$ and $3$ .

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

Multiply both sides of the equation by $\frac{4}{5}$ .

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

Simplify both sides of the equation.

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Simplify $\frac{4}{5} \cdot \frac{5 k}{4}$ .

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Cancel the common factor of $4$ .

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Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{5} \cdot (5 k) = \frac{4}{5} \cdot 5$

Cancel the common factor of $5$ .

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Factor $5$ out of $5 k$ .

$\frac{1}{5} \cdot (5 (k)) = \frac{4}{5} \cdot 5$

Cancel the common factor.

$\frac{1}{5} \cdot (5 k) = \frac{4}{5} \cdot 5$

Rewrite the expression.

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

Cancel the common factor of $5$ .

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Cancel the common factor.

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

Rewrite the expression.

$k = 4$

Solve for k 1/2k-3=2-3/4k

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