Solve for k |2k+6|=|k|

$| 2 k + 6 | = | k |$

Step 1

Rewrite the equation as $| k | = | 2 k + 6 |$ .

$| k | = | 2 k + 6 |$

Step 2

Rewrite the absolute value equation as four equations without absolute value bars.

$k = 2 k + 6$

$k = - (2 k + 6)$

$- k = 2 k + 6$

$- k = - (2 k + 6)$

Step 3

After simplifying, there are only two unique equations to be solved.

$k = 2 k + 6$

$k = - (2 k + 6)$

Step 4

Solve $k = 2 k + 6$ for $k$ .

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

Subtract $2 k$ from both sides of the equation.

$k - 2 k = 6$

Subtract $2 k$ from $k$ .

$- k = 6$

Divide each term in $- k = 6$ by $- 1$ and simplify.

Divide each term in $- k = 6$ by $- 1$ .

$\frac{- k}{- 1} = \frac{6}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{k}{1} = \frac{6}{- 1}$

Divide $k$ by $1$ .

$k = \frac{6}{- 1}$

Simplify the right side.

Divide $6$ by $- 1$ .

$k = - 6$

Step 5

Solve $k = - (2 k + 6)$ for $k$ .

Simplify $- (2 k + 6)$ .

Apply the distributive property.

$k = - (2 k) - 1 \cdot 6$

Multiply.

Multiply $2$ by $- 1$ .

$k = - 2 k - 1 \cdot 6$

Multiply $- 1$ by $6$ .

$k = - 2 k - 6$

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

Add $2 k$ to both sides of the equation.

$k + 2 k = - 6$

Add $k$ and $2 k$ .

$3 k = - 6$

Divide each term in $3 k = - 6$ by $3$ and simplify.

Divide each term in $3 k = - 6$ by $3$ .

$\frac{3 k}{3} = \frac{- 6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 k}{3} = \frac{- 6}{3}$

Divide $k$ by $1$ .

$k = \frac{- 6}{3}$

Simplify the right side.

Divide $- 6$ by $3$ .

$k = - 2$

Step 6

List all of the solutions.

$k = - 6, - 2$

Solve for k |2k+6|=|k|

Related Questions

Support LCMGCF.com by disabling your adblocker.