Solve for d 3|2d-9|-10=3

$3 | 2 d - 9 | - 10 = 3$

Move all terms not containing $| 2 d - 9 |$ to the right side of the equation.

Add $10$ to both sides of the equation.

$3 | 2 d - 9 | = 3 + 10$

Add $3$ and $10$ .

$3 | 2 d - 9 | = 13$

Divide each term in $3 | 2 d - 9 | = 13$ by $3$ and simplify.

Divide each term in $3 | 2 d - 9 | = 13$ by $3$ .

$\frac{3 | 2 d - 9 |}{3} = \frac{13}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 | 2 d - 9 |}{3} = \frac{13}{3}$

Divide $| 2 d - 9 |$ by $1$ .

$| 2 d - 9 | = \frac{13}{3}$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$2 d - 9 = \pm \frac{13}{3}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$2 d - 9 = \frac{13}{3}$

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

Add $9$ to both sides of the equation.

$2 d = \frac{13}{3} + 9$

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

$2 d = \frac{13}{3} + 9 \cdot \frac{3}{3}$

Combine $9$ and $\frac{3}{3}$ .

$2 d = \frac{13}{3} + \frac{9 \cdot 3}{3}$

Combine the numerators over the common denominator.

$2 d = \frac{13 + 9 \cdot 3}{3}$

Simplify the numerator.

Multiply $9$ by $3$ .

$2 d = \frac{13 + 27}{3}$

Add $13$ and $27$ .

$2 d = \frac{40}{3}$

Divide each term in $2 d = \frac{40}{3}$ by $2$ and simplify.

Divide each term in $2 d = \frac{40}{3}$ by $2$ .

$\frac{2 d}{2} = \frac{\frac{40}{3}}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 d}{2} = \frac{\frac{40}{3}}{2}$

Divide $d$ by $1$ .

$d = \frac{\frac{40}{3}}{2}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$d = \frac{40}{3} \cdot \frac{1}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $40$ .

$d = \frac{2 (20)}{3} \cdot \frac{1}{2}$

Cancel the common factor.

$d = \frac{2 \cdot 20}{3} \cdot \frac{1}{2}$

Rewrite the expression.

$d = \frac{20}{3}$

Next, use the negative value of the $\pm$ to find the second solution.

$2 d - 9 = - \frac{13}{3}$

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

Add $9$ to both sides of the equation.

$2 d = - \frac{13}{3} + 9$

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

$2 d = - \frac{13}{3} + 9 \cdot \frac{3}{3}$

Combine $9$ and $\frac{3}{3}$ .

$2 d = - \frac{13}{3} + \frac{9 \cdot 3}{3}$

Combine the numerators over the common denominator.

$2 d = \frac{- 13 + 9 \cdot 3}{3}$

Simplify the numerator.

Multiply $9$ by $3$ .

$2 d = \frac{- 13 + 27}{3}$

Add $- 13$ and $27$ .

$2 d = \frac{14}{3}$

Divide each term in $2 d = \frac{14}{3}$ by $2$ and simplify.

Divide each term in $2 d = \frac{14}{3}$ by $2$ .

$\frac{2 d}{2} = \frac{\frac{14}{3}}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 d}{2} = \frac{\frac{14}{3}}{2}$

Divide $d$ by $1$ .

$d = \frac{\frac{14}{3}}{2}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$d = \frac{14}{3} \cdot \frac{1}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $14$ .

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

Cancel the common factor.

$d = \frac{2 \cdot 7}{3} \cdot \frac{1}{2}$

Rewrite the expression.

$d = \frac{7}{3}$

The complete solution is the result of both the positive and negative portions of the solution.

$d = \frac{20}{3}, \frac{7}{3}$

The result can be shown in multiple forms.

Exact Form:

$d = \frac{20}{3}, \frac{7}{3}$

Decimal Form:

$d = 6.\overline{6}, 2.\overline{3}$

Mixed Number Form:

$d = 6 \frac{2}{3}, 2 \frac{1}{3}$

Solve for d 3|2d-9|-10=3

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