Solve for d -1/2d+3/8-d=1/4+3/4d+2

$- \frac{1}{2} d + \frac{3}{8} - d = \frac{1}{4} + \frac{3}{4} d + 2$

Step 1

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

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

$- \frac{d}{2} + \frac{3}{8} - d = \frac{1}{4} + \frac{3}{4} d + 2$

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

$- \frac{d}{2} - d \cdot \frac{2}{2} + \frac{3}{8} = \frac{1}{4} + \frac{3}{4} d + 2$

Simplify terms.

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

$- \frac{d}{2} + \frac{- d \cdot 2}{2} + \frac{3}{8} = \frac{1}{4} + \frac{3}{4} d + 2$

Combine the numerators over the common denominator.

$\frac{- d - d \cdot 2}{2} + \frac{3}{8} = \frac{1}{4} + \frac{3}{4} d + 2$

Simplify each term.

Simplify the numerator.

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

Factor $d$ out of $- d$ .

$\frac{d \cdot - 1 - d \cdot 2}{2} + \frac{3}{8} = \frac{1}{4} + \frac{3}{4} d + 2$

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

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

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

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

Multiply $- 1$ by $2$ .

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

Subtract $2$ from $- 1$ .

$\frac{d \cdot - 3}{2} + \frac{3}{8} = \frac{1}{4} + \frac{3}{4} d + 2$

Move $- 3$ to the left of $d$ .

$\frac{- 3 \cdot d}{2} + \frac{3}{8} = \frac{1}{4} + \frac{3}{4} d + 2$

Move the negative in front of the fraction.

$- \frac{3 d}{2} + \frac{3}{8} = \frac{1}{4} + \frac{3}{4} d + 2$

Step 2

Simplify $\frac{1}{4} + \frac{3}{4} d + 2$ .

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

$- \frac{3 d}{2} + \frac{3}{8} = \frac{1}{4} + \frac{3 d}{4} + 2$

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{3 d}{2} + \frac{3}{8} = \frac{3 d}{4} + \frac{1}{4} + 2 \cdot \frac{4}{4}$

Combine $2$ and $\frac{4}{4}$ .

$- \frac{3 d}{2} + \frac{3}{8} = \frac{3 d}{4} + \frac{1}{4} + \frac{2 \cdot 4}{4}$

Combine the numerators over the common denominator.

$- \frac{3 d}{2} + \frac{3}{8} = \frac{3 d}{4} + \frac{1 + 2 \cdot 4}{4}$

Simplify the numerator.

Multiply $2$ by $4$ .

$- \frac{3 d}{2} + \frac{3}{8} = \frac{3 d}{4} + \frac{1 + 8}{4}$

Add $1$ and $8$ .

$- \frac{3 d}{2} + \frac{3}{8} = \frac{3 d}{4} + \frac{9}{4}$

Step 3

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

Subtract $\frac{3 d}{4}$ from both sides of the equation.

$- \frac{3 d}{2} + \frac{3}{8} - \frac{3 d}{4} = \frac{9}{4}$

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

$- \frac{3 d}{2} \cdot \frac{2}{2} - \frac{3 d}{4} + \frac{3}{8} = \frac{9}{4}$

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

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

$- \frac{3 d \cdot 2}{2 \cdot 2} - \frac{3 d}{4} + \frac{3}{8} = \frac{9}{4}$

Multiply $2$ by $2$ .

$- \frac{3 d \cdot 2}{4} - \frac{3 d}{4} + \frac{3}{8} = \frac{9}{4}$

Combine the numerators over the common denominator.

$\frac{- 3 d \cdot 2 - 3 d}{4} + \frac{3}{8} = \frac{9}{4}$

Simplify each term.

Simplify the numerator.

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

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

$\frac{3 d (- 1 \cdot 2) - 3 d}{4} + \frac{3}{8} = \frac{9}{4}$

Factor $3 d$ out of $- 3 d$ .

$\frac{3 d (- 1 \cdot 2) + 3 d (- 1)}{4} + \frac{3}{8} = \frac{9}{4}$

Factor $3 d$ out of $3 d (- 1 \cdot 2) + 3 d (- 1)$ .

$\frac{3 d (- 1 \cdot 2 - 1)}{4} + \frac{3}{8} = \frac{9}{4}$

Multiply $- 1$ by $2$ .

$\frac{3 d (- 2 - 1)}{4} + \frac{3}{8} = \frac{9}{4}$

Subtract $1$ from $- 2$ .

$\frac{3 d \cdot - 3}{4} + \frac{3}{8} = \frac{9}{4}$

Multiply $- 3$ by $3$ .

$\frac{- 9 d}{4} + \frac{3}{8} = \frac{9}{4}$

Move the negative in front of the fraction.

$- \frac{9 d}{4} + \frac{3}{8} = \frac{9}{4}$

Step 4

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

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

$- \frac{9 d}{4} = \frac{9}{4} - \frac{3}{8}$

To write $\frac{9}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{9 d}{4} = \frac{9}{4} \cdot \frac{2}{2} - \frac{3}{8}$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{9}{4}$ by $\frac{2}{2}$ .

$- \frac{9 d}{4} = \frac{9 \cdot 2}{4 \cdot 2} - \frac{3}{8}$

Multiply $4$ by $2$ .

$- \frac{9 d}{4} = \frac{9 \cdot 2}{8} - \frac{3}{8}$

Combine the numerators over the common denominator.

$- \frac{9 d}{4} = \frac{9 \cdot 2 - 3}{8}$

Simplify the numerator.

Multiply $9$ by $2$ .

$- \frac{9 d}{4} = \frac{18 - 3}{8}$

Subtract $3$ from $18$ .

$- \frac{9 d}{4} = \frac{15}{8}$

Step 5

Multiply both sides of the equation by $- \frac{4}{9}$ .

$- \frac{4}{9} (- \frac{9 d}{4}) = - \frac{4}{9} \cdot \frac{15}{8}$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{4}{9} (- \frac{9 d}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{9}$ into the numerator.

$\frac{- 4}{9} (- \frac{9 d}{4}) = - \frac{4}{9} \cdot \frac{15}{8}$

Move the leading negative in $- \frac{9 d}{4}$ into the numerator.

$\frac{- 4}{9} \cdot \frac{- 9 d}{4} = - \frac{4}{9} \cdot \frac{15}{8}$

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{9} \cdot \frac{- 9 d}{4} = - \frac{4}{9} \cdot \frac{15}{8}$

Cancel the common factor.

$\frac{4 \cdot - 1}{9} \cdot \frac{- 9 d}{4} = - \frac{4}{9} \cdot \frac{15}{8}$

Rewrite the expression.

$\frac{- 1}{9} (- 9 d) = - \frac{4}{9} \cdot \frac{15}{8}$

Cancel the common factor of $9$ .

Factor $9$ out of $- 9 d$ .

$\frac{- 1}{9} (9 (- d)) = - \frac{4}{9} \cdot \frac{15}{8}$

Cancel the common factor.

$\frac{- 1}{9} (9 (- d)) = - \frac{4}{9} \cdot \frac{15}{8}$

Rewrite the expression.

$- - d = - \frac{4}{9} \cdot \frac{15}{8}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 d = - \frac{4}{9} \cdot \frac{15}{8}$

Multiply $d$ by $1$ .

$d = - \frac{4}{9} \cdot \frac{15}{8}$

Simplify the right side.

Simplify $- \frac{4}{9} \cdot \frac{15}{8}$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{9}$ into the numerator.

$d = \frac{- 4}{9} \cdot \frac{15}{8}$

Factor $4$ out of $- 4$ .

$d = \frac{4 (- 1)}{9} \cdot \frac{15}{8}$

Factor $4$ out of $8$ .

$d = \frac{4 \cdot - 1}{9} \cdot \frac{15}{4 \cdot 2}$

Cancel the common factor.

$d = \frac{4 \cdot - 1}{9} \cdot \frac{15}{4 \cdot 2}$

Rewrite the expression.

$d = \frac{- 1}{9} \cdot \frac{15}{2}$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$d = \frac{- 1}{3 (3)} \cdot \frac{15}{2}$

Factor $3$ out of $15$ .

$d = \frac{- 1}{3 \cdot 3} \cdot \frac{3 \cdot 5}{2}$

Cancel the common factor.

$d = \frac{- 1}{3 \cdot 3} \cdot \frac{3 \cdot 5}{2}$

Rewrite the expression.

$d = \frac{- 1}{3} \cdot \frac{5}{2}$

Multiply $\frac{- 1}{3}$ by $\frac{5}{2}$ .

$d = \frac{- 1 \cdot 5}{3 \cdot 2}$

Simplify the expression.

Multiply $- 1$ by $5$ .

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

Multiply $3$ by $2$ .

$d = \frac{- 5}{6}$

Move the negative in front of the fraction.

$d = - \frac{5}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$d = - \frac{5}{6}$

Decimal Form:

$d = - 0.8\overline{3}$

Solve for d -1/2d+3/8-d=1/4+3/4d+2

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