Basic Math Examples

$| z + 10 | = | z - 8 |$

Step 1

Rewrite the equation as $| z - 8 | = | z + 10 |$ .

$| z - 8 | = | z + 10 |$

Step 2

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

$z - 8 = z + 10$

$z - 8 = - (z + 10)$

$- (z - 8) = z + 10$

$- (z - 8) = - (z + 10)$

Step 3

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

$z - 8 = z + 10$

$z - 8 = - (z + 10)$

Step 4

Solve $z - 8 = z + 10$ 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.

$z - 8 - z = 10$

Step 4.1.2

Combine the opposite terms in $z - 8 - z$ .

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Step 4.1.2.1

Subtract $z$ from $z$ .

$0 - 8 = 10$

Step 4.1.2.2

Subtract $8$ from $0$ .

$- 8 = 10$

Step 4.2

Since $- 8 \neq 10$ , there are no solutions.

No solution

Step 5

Solve $z - 8 = - (z + 10)$ for $z$ .

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Step 5.1

Simplify $- (z + 10)$ .

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Step 5.1.1

Rewrite.

$z - 8 = 0 + 0 - (z + 10)$

Step 5.1.2

Simplify by adding zeros.

$z - 8 = - (z + 10)$

Step 5.1.3

Apply the distributive property.

$z - 8 = - z - 1 \cdot 10$

Step 5.1.4

Multiply $- 1$ by $10$ .

$z - 8 = - z - 10$

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.

$z - 8 + z = - 10$

Step 5.2.2

Add $z$ and $z$ .

$2 z - 8 = - 10$

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 $8$ to both sides of the equation.

$2 z = - 10 + 8$

Step 5.3.2

Add $- 10$ and $8$ .

$2 z = - 2$

Step 5.4

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

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Step 5.4.1

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

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

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.

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

Step 5.4.2.1.2

Divide $z$ by $1$ .

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

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Divide $- 2$ by $2$ .

$z = - 1$