Solve for z |z+9|=|z-9|

$| z + 9 | = | z - 9 |$

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

$z + 9 = z - 9$

$z + 9 = - (z - 9)$

$- (z + 9) = z - 9$

$- (z + 9) = - (z - 9)$

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

$z + 9 = z - 9$

$z + 9 = - (z - 9)$

Solve $z + 9 = z - 9$ for $z$ .

Tap for more steps…

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

Tap for more steps…

Subtract $z$ from both sides of the equation.

$z + 9 - z = - 9$

Combine the opposite terms in $z + 9 - z$ .

Tap for more steps…

Subtract $z$ from $z$ .

$0 + 9 = - 9$

Add $0$ and $9$ .

$9 = - 9$

Since $9 \neq - 9$ , there are no solutions.

No solution

Solve $z + 9 = - (z - 9)$ for $z$ .

Tap for more steps…

Simplify $- (z - 9)$ .

Tap for more steps…

Apply the distributive property.

$z + 9 = - z - - 9$

Multiply $- 1$ by $- 9$ .

$z + 9 = - z + 9$

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

Tap for more steps…

Add $z$ to both sides of the equation.

$z + 9 + z = 9$

Add $z$ and $z$ .

$2 z + 9 = 9$

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

Tap for more steps…

Subtract $9$ from both sides of the equation.

$2 z = 9 - 9$

Subtract $9$ from $9$ .

$2 z = 0$

Divide each term by $2$ and simplify.

Tap for more steps…

Divide each term in $2 z = 0$ by $2$ .

$\frac{2 z}{2} = \frac{0}{2}$

Cancel the common factor of $2$ .

Tap for more steps…

Cancel the common factor.

$\frac{2 z}{2} = \frac{0}{2}$

Divide $z$ by $1$ .

$z = \frac{0}{2}$

Divide $0$ by $2$ .

$z = 0$

List all of the solutions.

$z = 0$

Verify each of the solutions by substituting them into $| z + 9 | = | z - 9 |$ and solving.

$z = 0$

Solve for z |z+9|=|z-9|

Meet the Team our Math Expers

Our Professionals

Robert Kristofer

Anna Frok

Magnus Flores

Lydia Fran

We are MathExperts

We can solve all your math problems