Solve for k 10-10|-8k+4|=10

$10 - 10 | - 8 k + 4 | = 10$

Move all terms not containing $| - 8 k + 4 |$ to the right side of the equation.

Subtract $10$ from both sides of the equation.

$- 10 | - 8 k + 4 | = 10 - 10$

Subtract $10$ from $10$ .

$- 10 | - 8 k + 4 | = 0$

Divide each term in $- 10 | - 8 k + 4 | = 0$ by $- 10$ and simplify.

Divide each term in $- 10 | - 8 k + 4 | = 0$ by $- 10$ .

$\frac{- 10 | - 8 k + 4 |}{- 10} = \frac{0}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 | - 8 k + 4 |}{- 10} = \frac{0}{- 10}$

Divide $| - 8 k + 4 |$ by $1$ .

$| - 8 k + 4 | = \frac{0}{- 10}$

Simplify the right side.

Divide $0$ by $- 10$ .

$| - 8 k + 4 | = 0$

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

$- 8 k + 4 = \pm 0$

Plus or minus $0$ is $0$ .

$- 8 k + 4 = 0$

Subtract $4$ from both sides of the equation.

$- 8 k = - 4$

Divide each term in $- 8 k = - 4$ by $- 8$ and simplify.

Divide each term in $- 8 k = - 4$ by $- 8$ .

$\frac{- 8 k}{- 8} = \frac{- 4}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 k}{- 8} = \frac{- 4}{- 8}$

Divide $k$ by $1$ .

$k = \frac{- 4}{- 8}$

Simplify the right side.

Cancel the common factor of $- 4$ and $- 8$ .

Factor $- 4$ out of $- 4$ .

$k = \frac{- 4 (1)}{- 8}$

Cancel the common factors.

Factor $- 4$ out of $- 8$ .

$k = \frac{- 4 \cdot 1}{- 4 \cdot 2}$

Cancel the common factor.

$k = \frac{- 4 \cdot 1}{- 4 \cdot 2}$

Rewrite the expression.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$k = 0.5$

Solve for k 10-10|-8k+4|=10

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