Solve for d (3d-2)/8=-d+16 1/4

$\frac{3 d - 2}{8} = - d + 16 \frac{1}{4}$

Step 1

Simplify the right side.

Convert $16 \frac{1}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{3 d - 2}{8} = - d + 16 + \frac{1}{4}$

Add $16$ and $\frac{1}{4}$ .

To write $16$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 d - 2}{8} = - d + 16 \cdot \frac{4}{4} + \frac{1}{4}$

Combine $16$ and $\frac{4}{4}$ .

$\frac{3 d - 2}{8} = - d + \frac{16 \cdot 4}{4} + \frac{1}{4}$

Combine the numerators over the common denominator.

$\frac{3 d - 2}{8} = - d + \frac{16 \cdot 4 + 1}{4}$

Simplify the numerator.

Multiply $16$ by $4$ .

$\frac{3 d - 2}{8} = - d + \frac{64 + 1}{4}$

Add $64$ and $1$ .

$\frac{3 d - 2}{8} = - d + \frac{65}{4}$

Step 2

Multiply both sides by $8$ .

$\frac{3 d - 2}{8} \cdot 8 = (- d + \frac{65}{4}) \cdot 8$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{3 d - 2}{8} \cdot 8 = (- d + \frac{65}{4}) \cdot 8$

Rewrite the expression.

$3 d - 2 = (- d + \frac{65}{4}) \cdot 8$

Simplify the right side.

Simplify $(- d + \frac{65}{4}) \cdot 8$ .

Apply the distributive property.

$3 d - 2 = - d \cdot 8 + \frac{65}{4} \cdot 8$

Multiply $8$ by $- 1$ .

$3 d - 2 = - 8 d + \frac{65}{4} \cdot 8$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$3 d - 2 = - 8 d + \frac{65}{4} \cdot (4 (2))$

Cancel the common factor.

$3 d - 2 = - 8 d + \frac{65}{4} \cdot (4 \cdot 2)$

Rewrite the expression.

$3 d - 2 = - 8 d + 65 \cdot 2$

Multiply $65$ by $2$ .

$3 d - 2 = - 8 d + 130$

Step 4

Solve for $d$ .

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

Add $8 d$ to both sides of the equation.

$3 d - 2 + 8 d = 130$

Add $3 d$ and $8 d$ .

$11 d - 2 = 130$

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

Add $2$ to both sides of the equation.

$11 d = 130 + 2$

Add $130$ and $2$ .

$11 d = 132$

Divide each term in $11 d = 132$ by $11$ and simplify.

Divide each term in $11 d = 132$ by $11$ .

$\frac{11 d}{11} = \frac{132}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 d}{11} = \frac{132}{11}$

Divide $d$ by $1$ .

$d = \frac{132}{11}$

Simplify the right side.

Divide $132$ by $11$ .

$d = 12$

Solve for d (3d-2)/8=-d+16 1/4

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