Solve for d |-7d-8|=9d+3

$| - 7 d - 8 | = 9 d + 3$

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

$- 7 d - 8 = \pm (9 d + 3)$

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.

$- 7 d - 8 = 9 d + 3$

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

Subtract $9 d$ from both sides of the equation.

$- 7 d - 8 - 9 d = 3$

Subtract $9 d$ from $- 7 d$ .

$- 16 d - 8 = 3$

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

Add $8$ to both sides of the equation.

$- 16 d = 3 + 8$

Add $3$ and $8$ .

$- 16 d = 11$

Divide each term in $- 16 d = 11$ by $- 16$ and simplify.

Divide each term in $- 16 d = 11$ by $- 16$ .

$\frac{- 16 d}{- 16} = \frac{11}{- 16}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 d}{- 16} = \frac{11}{- 16}$

Divide $d$ by $1$ .

$d = \frac{11}{- 16}$

Simplify the right side.

Move the negative in front of the fraction.

$d = - \frac{11}{16}$

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

$- 7 d - 8 = - (9 d + 3)$

Simplify $- (9 d + 3)$ .

Rewrite.

$- 7 d - 8 = 0 + 0 - (9 d + 3)$

Simplify by adding zeros.

$- 7 d - 8 = - (9 d + 3)$

Apply the distributive property.

$- 7 d - 8 = - (9 d) - 1 \cdot 3$

Multiply.

Multiply $9$ by $- 1$ .

$- 7 d - 8 = - 9 d - 1 \cdot 3$

Multiply $- 1$ by $3$ .

$- 7 d - 8 = - 9 d - 3$

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

Add $9 d$ to both sides of the equation.

$- 7 d - 8 + 9 d = - 3$

Add $- 7 d$ and $9 d$ .

$2 d - 8 = - 3$

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

Add $8$ to both sides of the equation.

$2 d = - 3 + 8$

Add $- 3$ and $8$ .

$2 d = 5$

Divide each term in $2 d = 5$ by $2$ and simplify.

Divide each term in $2 d = 5$ by $2$ .

$\frac{2 d}{2} = \frac{5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 d}{2} = \frac{5}{2}$

Divide $d$ by $1$ .

$d = \frac{5}{2}$

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

$d = - \frac{11}{16}, \frac{5}{2}$

Exclude the solutions that do not make $| - 7 d - 8 | = 9 d + 3$ true.

$d = \frac{5}{2}$

The result can be shown in multiple forms.

Exact Form:

$d = \frac{5}{2}$

Decimal Form:

$d = 2.5$

Mixed Number Form:

$d = 2 \frac{1}{2}$

Solve for d |-7d-8|=9d+3

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