Algebra Examples

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

Step 1

Simplify $\frac{1}{2} d$ .

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

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

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

Step 2

Combine $\frac{2}{3}$ and $d$ .

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

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

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Step 3.4.1

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

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

Step 3.4.2

Multiply $2$ by $3$ .

$\frac{d \cdot 3}{6} - \frac{2 d}{3} \cdot \frac{2}{2} = - 8$

Step 3.4.3

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

$\frac{d \cdot 3}{6} - \frac{2 d \cdot 2}{3 \cdot 2} = - 8$

Step 3.4.4

Multiply $3$ by $2$ .

$\frac{d \cdot 3}{6} - \frac{2 d \cdot 2}{6} = - 8$

Step 3.5

Combine the numerators over the common denominator.

$\frac{d \cdot 3 - 2 d \cdot 2}{6} = - 8$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Factor $d$ out of $d \cdot 3 - 2 d \cdot 2$ .

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Step 3.6.1.1

Factor $d$ out of $d \cdot 3$ .

$\frac{d (3) - 2 d \cdot 2}{6} = - 8$

Step 3.6.1.2

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

$\frac{d (3) + d (- 2 \cdot 2)}{6} = - 8$

Step 3.6.1.3

Factor $d$ out of $d (3) + d (- 2 \cdot 2)$ .

$\frac{d (3 - 2 \cdot 2)}{6} = - 8$

Step 3.6.2

Multiply $- 2$ by $2$ .

$\frac{d (3 - 4)}{6} = - 8$

Step 3.6.3

Subtract $4$ from $3$ .

$\frac{d \cdot - 1}{6} = - 8$

Step 3.7

Move $- 1$ to the left of $d$ .

$\frac{- 1 \cdot d}{6} = - 8$

Step 3.8

Move the negative in front of the fraction.

$- \frac{d}{6} = - 8$

Step 4

Multiply both sides of the equation by $- 6$ .

$- 6 (- \frac{d}{6}) = - 6 \cdot - 8$

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 $- 6 (- \frac{d}{6})$ .

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Step 5.1.1.1

Cancel the common factor of $6$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{d}{6}$ into the numerator.

$- 6 \frac{- d}{6} = - 6 \cdot - 8$

Step 5.1.1.1.2

Factor $6$ out of $- 6$ .

$6 (- 1) \frac{- d}{6} = - 6 \cdot - 8$

Step 5.1.1.1.3

Cancel the common factor.

$6 \cdot - 1 \frac{- d}{6} = - 6 \cdot - 8$

Step 5.1.1.1.4

Rewrite the expression.

$- - d = - 6 \cdot - 8$

Step 5.1.1.2

Multiply.

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Step 5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 d = - 6 \cdot - 8$

Step 5.1.1.2.2

Multiply $d$ by $1$ .

$d = - 6 \cdot - 8$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 6$ by $- 8$ .

$d = 48$