Basic Math Examples

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

Step 1

Rewrite the equation as

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

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

Step 2

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

$z - 9 = z + 9$

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

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

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

Step 3

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

$z - 9 = z + 9$

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

Step 4

Solve

$z - 9 = z + 9$ for

$z$ .

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Step 4.1

Move all terms containing

$z$ to the left side of the equation.

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Step 4.1.1

Subtract

$z$ from both sides of the equation.

$z - 9 - z = 9$

Step 4.1.2

Combine the opposite terms in

$z - 9 - z$ .

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Step 4.1.2.1

Subtract

$z$ from

$z$ .

$0 - 9 = 9$

Step 4.1.2.2

Subtract

$9$ from

$0$ .

$- 9 = 9$

$- 9 = 9$

$- 9 = 9$

Step 4.2

Since

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

No solution

No solution

Step 5

Solve

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

$z$ .

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Step 5.1

Simplify

$- (z + 9)$ .

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Step 5.1.1

Rewrite.

$z - 9 = 0 + 0 - (z + 9)$

Step 5.1.2

Simplify by adding zeros.

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

Step 5.1.3

Apply the distributive property.

$z - 9 = - z - 1 \cdot 9$

Step 5.1.4

Multiply

$- 1$ by

$9$ .

$z - 9 = - z - 9$

$z - 9 = - z - 9$

Step 5.2

Move all terms containing

$z$ to the left side of the equation.

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Step 5.2.1

Add

$z$ to both sides of the equation.

$z - 9 + z = - 9$

Step 5.2.2

Add

$z$ and

$z$ .

$2 z - 9 = - 9$

$2 z - 9 = - 9$

Step 5.3

Move all terms not containing

$z$ to the right side of the equation.

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Step 5.3.1

Add

$9$ to both sides of the equation.

$2 z = - 9 + 9$

Step 5.3.2

Add

$- 9$ and

$9$ .

$2 z = 0$

$2 z = 0$

Step 5.4

Divide each term in

$2 z = 0$ by

$2$ and simplify.

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Step 5.4.1

Divide each term in

$2 z = 0$ by

$2$ .

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

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Cancel the common factor of

$2$ .

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Step 5.4.2.1.1

Cancel the common factor.

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

Step 5.4.2.1.2

Divide

$z$ by

$1$ .

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

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

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

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Divide

$0$ by

$2$ .

$z = 0$

$z = 0$

$z = 0$

$z = 0$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$