Solve Graphically 1/3(d-4)-3/2(3d-3)=7/12

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Solve Graphically 1/3*(d-4)-3/2*(3d-3)=7/12

$\frac{1}{3} \cdot (d - 4) - \frac{3}{2} \cdot (3 d - 3) = \frac{7}{12}$

Simplify $\frac{1}{3} \cdot (d - 4) - \frac{3}{2} \cdot (3 d - 3)$ .

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Simplify each term.

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Apply the distributive property.

$\frac{1}{3} d + \frac{1}{3} \cdot - 4 - \frac{3}{2} \cdot (3 d - 3) = \frac{7}{12}$

Combine $\frac{1}{3}$ and $d$ .

$\frac{d}{3} + \frac{1}{3} \cdot - 4 - \frac{3}{2} \cdot (3 d - 3) = \frac{7}{12}$

Combine $\frac{1}{3}$ and $- 4$ .

$\frac{d}{3} + \frac{- 4}{3} - \frac{3}{2} \cdot (3 d - 3) = \frac{7}{12}$

Move the negative in front of the fraction.

$\frac{d}{3} - \frac{4}{3} - \frac{3}{2} \cdot (3 d - 3) = \frac{7}{12}$

Apply the distributive property.

$\frac{d}{3} - \frac{4}{3} - \frac{3}{2} (3 d) - \frac{3}{2} \cdot - 3 = \frac{7}{12}$

Multiply $- \frac{3}{2} (3 d)$ .

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Multiply $3$ by $- 1$ .

$\frac{d}{3} - \frac{4}{3} - 3 (\frac{3}{2}) d - \frac{3}{2} \cdot - 3 = \frac{7}{12}$

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

$\frac{d}{3} - \frac{4}{3} + \frac{- 3 \cdot 3}{2} d - \frac{3}{2} \cdot - 3 = \frac{7}{12}$

Multiply $- 3$ by $3$ .

$\frac{d}{3} - \frac{4}{3} + \frac{- 9}{2} d - \frac{3}{2} \cdot - 3 = \frac{7}{12}$

Combine $\frac{- 9}{2}$ and $d$ .

$\frac{d}{3} - \frac{4}{3} + \frac{- 9 d}{2} - \frac{3}{2} \cdot - 3 = \frac{7}{12}$

Multiply $- \frac{3}{2} \cdot - 3$ .

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Multiply $- 3$ by $- 1$ .

$\frac{d}{3} - \frac{4}{3} + \frac{- 9 d}{2} + 3 (\frac{3}{2}) = \frac{7}{12}$

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

$\frac{d}{3} - \frac{4}{3} + \frac{- 9 d}{2} + \frac{3 \cdot 3}{2} = \frac{7}{12}$

Multiply $3$ by $3$ .

$\frac{d}{3} - \frac{4}{3} + \frac{- 9 d}{2} + \frac{9}{2} = \frac{7}{12}$

Move the negative in front of the fraction.

$\frac{d}{3} - \frac{4}{3} - \frac{9 d}{2} + \frac{9}{2} = \frac{7}{12}$

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

$\frac{d}{3} \cdot \frac{2}{2} - \frac{9 d}{2} - \frac{4}{3} + \frac{9}{2} = \frac{7}{12}$

To write $- \frac{9 d}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{d}{3} \cdot \frac{2}{2} - \frac{9 d}{2} \cdot \frac{3}{3} - \frac{4}{3} + \frac{9}{2} = \frac{7}{12}$

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

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

$\frac{d \cdot 2}{3 \cdot 2} - \frac{9 d}{2} \cdot \frac{3}{3} - \frac{4}{3} + \frac{9}{2} = \frac{7}{12}$

Multiply $3$ by $2$ .

$\frac{d \cdot 2}{6} - \frac{9 d}{2} \cdot \frac{3}{3} - \frac{4}{3} + \frac{9}{2} = \frac{7}{12}$

Multiply $\frac{9 d}{2}$ and $\frac{3}{3}$ .

$\frac{d \cdot 2}{6} - \frac{9 d \cdot 3}{2 \cdot 3} - \frac{4}{3} + \frac{9}{2} = \frac{7}{12}$

Multiply $2$ by $3$ .

$\frac{d \cdot 2}{6} - \frac{9 d \cdot 3}{6} - \frac{4}{3} + \frac{9}{2} = \frac{7}{12}$

Combine the numerators over the common denominator.

$\frac{d \cdot 2 - 9 d \cdot 3}{6} - \frac{4}{3} + \frac{9}{2} = \frac{7}{12}$

Simplify each term.

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Simplify the numerator.

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Factor $d$ out of $d \cdot 2 - 9 d \cdot 3$ .

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

$\frac{d (2) - 9 d \cdot 3}{6} - \frac{4}{3} + \frac{9}{2} = \frac{7}{12}$

Factor $d$ out of $- 9 d \cdot 3$ .

$\frac{d (2) + d (- 9 \cdot 3)}{6} - \frac{4}{3} + \frac{9}{2} = \frac{7}{12}$

Factor $d$ out of $d (2) + d (- 9 \cdot 3)$ .

$\frac{d (2 - 9 \cdot 3)}{6} - \frac{4}{3} + \frac{9}{2} = \frac{7}{12}$

Multiply $- 9$ by $3$ .

$\frac{d (2 - 27)}{6} - \frac{4}{3} + \frac{9}{2} = \frac{7}{12}$

Subtract $27$ from $2$ .

$\frac{d \cdot - 25}{6} - \frac{4}{3} + \frac{9}{2} = \frac{7}{12}$

Move $- 25$ to the left of $d$ .

$\frac{- 25 \cdot d}{6} - \frac{4}{3} + \frac{9}{2} = \frac{7}{12}$

Move the negative in front of the fraction.

$- \frac{25 d}{6} - \frac{4}{3} + \frac{9}{2} = \frac{7}{12}$

To write $- \frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{25 d}{6} - \frac{4}{3} \cdot \frac{2}{2} + \frac{9}{2} = \frac{7}{12}$

To write $\frac{9}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{25 d}{6} - \frac{4}{3} \cdot \frac{2}{2} + \frac{9}{2} \cdot \frac{3}{3} = \frac{7}{12}$

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

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Multiply $\frac{4}{3}$ and $\frac{2}{2}$ .

$- \frac{25 d}{6} - \frac{4 \cdot 2}{3 \cdot 2} + \frac{9}{2} \cdot \frac{3}{3} = \frac{7}{12}$

Multiply $3$ by $2$ .

$- \frac{25 d}{6} - \frac{4 \cdot 2}{6} + \frac{9}{2} \cdot \frac{3}{3} = \frac{7}{12}$

Multiply $\frac{9}{2}$ and $\frac{3}{3}$ .

$- \frac{25 d}{6} - \frac{4 \cdot 2}{6} + \frac{9 \cdot 3}{2 \cdot 3} = \frac{7}{12}$

Multiply $2$ by $3$ .

$- \frac{25 d}{6} - \frac{4 \cdot 2}{6} + \frac{9 \cdot 3}{6} = \frac{7}{12}$

Combine the numerators over the common denominator.

$- \frac{25 d}{6} + \frac{- 4 \cdot 2 + 9 \cdot 3}{6} = \frac{7}{12}$

Simplify the numerator.

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Multiply $- 4$ by $2$ .

$- \frac{25 d}{6} + \frac{- 8 + 9 \cdot 3}{6} = \frac{7}{12}$

Multiply $9$ by $3$ .

$- \frac{25 d}{6} + \frac{- 8 + 27}{6} = \frac{7}{12}$

Add $- 8$ and $27$ .

$- \frac{25 d}{6} + \frac{19}{6} = \frac{7}{12}$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$d \approx 0.61999999$

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