Solve for r 8-9|10r-9|=-73

$8 - 9 | 10 r - 9 | = - 73$

Step 1

Move all terms not containing $| 10 r - 9 |$ to the right side of the equation.

Subtract $8$ from both sides of the equation.

$- 9 | 10 r - 9 | = - 73 - 8$

Subtract $8$ from $- 73$ .

$- 9 | 10 r - 9 | = - 81$

Step 2

Divide each term in $- 9 | 10 r - 9 | = - 81$ by $- 9$ and simplify.

Divide each term in $- 9 | 10 r - 9 | = - 81$ by $- 9$ .

$\frac{- 9 | 10 r - 9 |}{- 9} = \frac{- 81}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 | 10 r - 9 |}{- 9} = \frac{- 81}{- 9}$

Divide $| 10 r - 9 |$ by $1$ .

$| 10 r - 9 | = \frac{- 81}{- 9}$

Simplify the right side.

Divide $- 81$ by $- 9$ .

$| 10 r - 9 | = 9$

Step 3

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

$10 r - 9 = \pm 9$

Step 4

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.

$10 r - 9 = 9$

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

Add $9$ to both sides of the equation.

$10 r = 9 + 9$

Add $9$ and $9$ .

$10 r = 18$

Divide each term in $10 r = 18$ by $10$ and simplify.

Divide each term in $10 r = 18$ by $10$ .

$\frac{10 r}{10} = \frac{18}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 r}{10} = \frac{18}{10}$

Divide $r$ by $1$ .

$r = \frac{18}{10}$

Simplify the right side.

Cancel the common factor of $18$ and $10$ .

Factor $2$ out of $18$ .

$r = \frac{2 (9)}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$r = \frac{2 \cdot 9}{2 \cdot 5}$

Cancel the common factor.

$r = \frac{2 \cdot 9}{2 \cdot 5}$

Rewrite the expression.

$r = \frac{9}{5}$

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

$10 r - 9 = - 9$

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

Add $9$ to both sides of the equation.

$10 r = - 9 + 9$

Add $- 9$ and $9$ .

$10 r = 0$

Divide each term in $10 r = 0$ by $10$ and simplify.

Divide each term in $10 r = 0$ by $10$ .

$\frac{10 r}{10} = \frac{0}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 r}{10} = \frac{0}{10}$

Divide $r$ by $1$ .

$r = \frac{0}{10}$

Simplify the right side.

Divide $0$ by $10$ .

$r = 0$

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

$r = \frac{9}{5}, 0$

Step 5

The result can be shown in multiple forms.

Exact Form:

$r = \frac{9}{5}, 0$

Decimal Form:

$r = 1.8, 0$

Mixed Number Form:

$r = 1 \frac{4}{5}, 0$

Solve for r 8-9|10r-9|=-73

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