Solve for k |2k+1|=5

$| 2 k + 1 | = 5$

Step 1

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

$2 k + 1 = \pm 5$

Step 2

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.

$2 k + 1 = 5$

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

Subtract $1$ from both sides of the equation.

$2 k = 5 - 1$

Subtract $1$ from $5$ .

$2 k = 4$

Divide each term in $2 k = 4$ by $2$ and simplify.

Divide each term in $2 k = 4$ by $2$ .

$\frac{2 k}{2} = \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 k}{2} = \frac{4}{2}$

Divide $k$ by $1$ .

$k = \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$k = 2$

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

$2 k + 1 = - 5$

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

Subtract $1$ from both sides of the equation.

$2 k = - 5 - 1$

Subtract $1$ from $- 5$ .

$2 k = - 6$

Divide each term in $2 k = - 6$ by $2$ and simplify.

Divide each term in $2 k = - 6$ by $2$ .

$\frac{2 k}{2} = \frac{- 6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 k}{2} = \frac{- 6}{2}$

Divide $k$ by $1$ .

$k = \frac{- 6}{2}$

Simplify the right side.

Divide $- 6$ by $2$ .

$k = - 3$

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

$k = 2, - 3$

Solve for k |2k+1|=5

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