Solve for m |8m-10|-9=1

$| 8 m - 10 | - 9 = 1$

Move all terms not containing $| 8 m - 10 |$ to the right side of the equation.

Add $9$ to both sides of the equation.

$| 8 m - 10 | = 1 + 9$

Add $1$ and $9$ .

$| 8 m - 10 | = 10$

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

$8 m - 10 = \pm 10$

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.

$8 m - 10 = 10$

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

Add $10$ to both sides of the equation.

$8 m = 10 + 10$

Add $10$ and $10$ .

$8 m = 20$

Divide each term in $8 m = 20$ by $8$ and simplify.

Divide each term in $8 m = 20$ by $8$ .

$\frac{8 m}{8} = \frac{20}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 m}{8} = \frac{20}{8}$

Divide $m$ by $1$ .

$m = \frac{20}{8}$

Simplify the right side.

Cancel the common factor of $20$ and $8$ .

Factor $4$ out of $20$ .

$m = \frac{4 (5)}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$m = \frac{4 \cdot 5}{4 \cdot 2}$

Cancel the common factor.

$m = \frac{4 \cdot 5}{4 \cdot 2}$

Rewrite the expression.

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

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

$8 m - 10 = - 10$

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

Add $10$ to both sides of the equation.

$8 m = - 10 + 10$

Add $- 10$ and $10$ .

$8 m = 0$

Divide each term in $8 m = 0$ by $8$ and simplify.

Divide each term in $8 m = 0$ by $8$ .

$\frac{8 m}{8} = \frac{0}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 m}{8} = \frac{0}{8}$

Divide $m$ by $1$ .

$m = \frac{0}{8}$

Simplify the right side.

Divide $0$ by $8$ .

$m = 0$

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

$m = \frac{5}{2}, 0$

The result can be shown in multiple forms.

Exact Form:

$m = \frac{5}{2}, 0$

Decimal Form:

$m = 2.5, 0$

Mixed Number Form:

$m = 2 \frac{1}{2}, 0$

Solve for m |8m-10|-9=1

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