Solve for j |j|=|2j+3|

$| j | = | 2 j + 3 |$

Rewrite the equation as $| 2 j + 3 | = | j |$ .

$| 2 j + 3 | = | j |$

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

$2 j + 3 = j$

$2 j + 3 = - j$

$- (2 j + 3) = j$

$- (2 j + 3) = - j$

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

$2 j + 3 = j$

$2 j + 3 = - j$

Solve $2 j + 3 = j$ for $j$ .

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

Subtract $j$ from both sides of the equation.

$2 j + 3 - j = 0$

Subtract $j$ from $2 j$ .

$j + 3 = 0$

Subtract $3$ from both sides of the equation.

$j = - 3$

Solve $2 j + 3 = - j$ for $j$ .

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

Add $j$ to both sides of the equation.

$2 j + 3 + j = 0$

Add $2 j$ and $j$ .

$3 j + 3 = 0$

Subtract $3$ from both sides of the equation.

$3 j = - 3$

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

Divide each term in $3 j = - 3$ by $3$ .

$\frac{3 j}{3} = \frac{- 3}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 j}{3} = \frac{- 3}{3}$

Divide $j$ by $1$ .

$j = \frac{- 3}{3}$

Simplify the right side.

Divide $- 3$ by $3$ .

$j = - 1$

List all of the solutions.

$j = - 3, - 1$