Finite Math Examples

$\frac{1}{2} d + \frac{3}{8} = - 2 d$

Step 1

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

$\frac{d}{2} + \frac{3}{8} = - 2 d$

Step 2

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

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Step 2.1

Add $2 d$ to both sides of the equation.

$\frac{d}{2} + \frac{3}{8} + 2 d = 0$

Step 2.2

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

$\frac{d}{2} + 2 d \cdot \frac{2}{2} + \frac{3}{8} = 0$

Step 2.3

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

$\frac{d}{2} + \frac{2 d \cdot 2}{2} + \frac{3}{8} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{d + 2 d \cdot 2}{2} + \frac{3}{8} = 0$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $d$ out of $d + 2 d \cdot 2$ .

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Step 2.5.1.1.1

Raise $d$ to the power of $1$ .

$\frac{d^{1} + 2 d \cdot 2}{2} + \frac{3}{8} = 0$

Step 2.5.1.1.2

Factor $d$ out of $d^{1}$ .

$\frac{d \cdot 1 + 2 d \cdot 2}{2} + \frac{3}{8} = 0$

Step 2.5.1.1.3

Factor $d$ out of $2 d \cdot 2$ .

$\frac{d \cdot 1 + d (2 \cdot 2)}{2} + \frac{3}{8} = 0$

Step 2.5.1.1.4

Factor $d$ out of $d \cdot 1 + d (2 \cdot 2)$ .

$\frac{d (1 + 2 \cdot 2)}{2} + \frac{3}{8} = 0$

Step 2.5.1.2

Multiply $2$ by $2$ .

$\frac{d (1 + 4)}{2} + \frac{3}{8} = 0$

Step 2.5.1.3

Add $1$ and $4$ .

$\frac{d \cdot 5}{2} + \frac{3}{8} = 0$

Step 2.5.2

Move $5$ to the left of $d$ .

$\frac{5 d}{2} + \frac{3}{8} = 0$

Step 3

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

$\frac{5 d}{2} = - \frac{3}{8}$

Step 4

Multiply both sides of the equation by $\frac{2}{5}$ .

$\frac{2}{5} \cdot \frac{5 d}{2} = \frac{2}{5} (- \frac{3}{8})$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{2}{5} \cdot \frac{5 d}{2}$ .

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Step 5.1.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{2}{5} \cdot \frac{5 d}{2} = \frac{2}{5} (- \frac{3}{8})$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 d) = \frac{2}{5} (- \frac{3}{8})$

Step 5.1.1.2

Cancel the common factor of $5$ .

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Step 5.1.1.2.1

Factor $5$ out of $5 d$ .

$\frac{1}{5} (5 (d)) = \frac{2}{5} (- \frac{3}{8})$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 d) = \frac{2}{5} (- \frac{3}{8})$

Step 5.1.1.2.3

Rewrite the expression.

$d = \frac{2}{5} (- \frac{3}{8})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{2}{5} (- \frac{3}{8})$ .

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Step 5.2.1.1

Cancel the common factor of $2$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{3}{8}$ into the numerator.

$d = \frac{2}{5} \cdot \frac{- 3}{8}$

Step 5.2.1.1.2

Factor $2$ out of $8$ .

$d = \frac{2}{5} \cdot \frac{- 3}{2 (4)}$

Step 5.2.1.1.3

Cancel the common factor.

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

Step 5.2.1.1.4

Rewrite the expression.

$d = \frac{1}{5} \cdot \frac{- 3}{4}$

Step 5.2.1.2

Multiply $\frac{1}{5}$ by $\frac{- 3}{4}$ .

$d = \frac{- 3}{5 \cdot 4}$

Step 5.2.1.3

Simplify the expression.

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Step 5.2.1.3.1

Multiply $5$ by $4$ .

$d = \frac{- 3}{20}$

Step 5.2.1.3.2

Move the negative in front of the fraction.

$d = - \frac{3}{20}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$d = - \frac{3}{20}$

Decimal Form:

$d = - 0.15$