Algebra Examples

$\frac{1}{2} k + 2 = 5 + \frac{5}{6} k$

Step 1

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

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

Step 2

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

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

Step 3

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

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Step 3.1

Subtract $\frac{5 k}{6}$ from both sides of the equation.

$\frac{k}{2} + 2 - \frac{5 k}{6} = 5$

Step 3.2

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

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

Step 3.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{k}{2}$ by $\frac{3}{3}$ .

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

Step 3.3.2

Multiply $2$ by $3$ .

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Subtract $5 k$ from $k \cdot 3$ .

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Step 3.5.1

Reorder $k$ and $3$ .

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

Step 3.5.2

Subtract $5 k$ from $3 \cdot k$ .

$\frac{- 2 \cdot k}{6} + 2 = 5$

Step 3.6

Simplify each term.

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Step 3.6.1

Cancel the common factor of $- 2$ and $6$ .

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Step 3.6.1.1

Factor $2$ out of $- 2 \cdot k$ .

$\frac{2 (- k)}{6} + 2 = 5$

Step 3.6.1.2

Cancel the common factors.

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Step 3.6.1.2.1

Factor $2$ out of $6$ .

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

Step 3.6.1.2.2

Cancel the common factor.

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

Step 3.6.1.2.3

Rewrite the expression.

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

Step 3.6.2

Move the negative in front of the fraction.

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

Step 4

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

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Step 4.1

Subtract $2$ from both sides of the equation.

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

Step 4.2

Subtract $2$ from $5$ .

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

Step 5

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{k}{3}) = - 3 \cdot 3$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $- 3 (- \frac{k}{3})$ .

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Step 6.1.1.1

Cancel the common factor of $3$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{k}{3}$ into the numerator.

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

Step 6.1.1.1.2

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- k}{3} = - 3 \cdot 3$

Step 6.1.1.1.3

Cancel the common factor.

$3 \cdot - 1 \frac{- k}{3} = - 3 \cdot 3$

Step 6.1.1.1.4

Rewrite the expression.

$- - k = - 3 \cdot 3$

Step 6.1.1.2

Multiply.

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Step 6.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 k = - 3 \cdot 3$

Step 6.1.1.2.2

Multiply $k$ by $1$ .

$k = - 3 \cdot 3$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $- 3$ by $3$ .

$k = - 9$