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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Name

Name	one billion nine hundred forty-five million one hundred sixty-six thousand four hundred eighty-three

Interesting facts

1945166483 has 8 divisors, whose sum is 2096435376
The reverse of 1945166483 is 3846615491
Previous prime number is 1291

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 47
Digital Root 2

Name

Name	one billion nine hundred thirty-two million seven hundred sixteen thousand seven hundred thirty

Interesting facts

1932716730 has 16 divisors, whose sum is 3534110976
The reverse of 1932716730 is 0376172391
Previous prime number is 7

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 39
Digital Root 3

Name

Name	one billion one hundred seventy-nine million forty-two thousand eight hundred fifty-two

Interesting facts

1179042852 has 32 divisors, whose sum is 3809215872
The reverse of 1179042852 is 2582409711
Previous prime number is 13

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 39
Digital Root 3

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