Basic Math Examples

$\frac{2}{7} k - \frac{3}{8} = - \frac{19}{8}$

Step 1

Combine $\frac{2}{7}$ and $k$ .

$\frac{2 k}{7} - \frac{3}{8} = - \frac{19}{8}$

Step 2

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

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Step 2.1

Add $\frac{3}{8}$ to both sides of the equation.

$\frac{2 k}{7} = - \frac{19}{8} + \frac{3}{8}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{2 k}{7} = \frac{- 19 + 3}{8}$

Step 2.3

Add $- 19$ and $3$ .

$\frac{2 k}{7} = \frac{- 16}{8}$

Step 2.4

Divide $- 16$ by $8$ .

$\frac{2 k}{7} = - 2$

Step 3

Multiply both sides of the equation by $\frac{7}{2}$ .

$\frac{7}{2} \cdot \frac{2 k}{7} = \frac{7}{2} \cdot - 2$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{7}{2} \cdot \frac{2 k}{7}$ .

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Step 4.1.1.1

Cancel the common factor of $7$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{7}{2} \cdot \frac{2 k}{7} = \frac{7}{2} \cdot - 2$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 k) = \frac{7}{2} \cdot - 2$

Step 4.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.2.1

Factor $2$ out of $2 k$ .

$\frac{1}{2} (2 (k)) = \frac{7}{2} \cdot - 2$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 k) = \frac{7}{2} \cdot - 2$

Step 4.1.1.2.3

Rewrite the expression.

$k = \frac{7}{2} \cdot - 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{7}{2} \cdot - 2$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Factor $2$ out of $- 2$ .

$k = \frac{7}{2} \cdot (2 (- 1))$

Step 4.2.1.1.2

Cancel the common factor.

$k = \frac{7}{2} \cdot (2 \cdot - 1)$

Step 4.2.1.1.3

Rewrite the expression.

$k = 7 \cdot - 1$

Step 4.2.1.2

Multiply $7$ by $- 1$ .

$k = - 7$