Basic Math Examples

| z + 10 | = | z - 8 |

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

Step 1

Rewrite the equation as

| z - 8 | = | z + 10 |

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

| 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)

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

- (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

$z - 8 = z + 10$

z - 8 = - (z + 10)

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

Step 4

Solve

z - 8 = z + 10

$z - 8 = z + 10$ for

z

$z$ .

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Step 4.1

Move all terms containing

z

$z$ to the left side of the equation.

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Step 4.1.1

Subtract

z

$z$ from both sides of the equation.

z - 8 - z = 10

$z - 8 - z = 10$

Step 4.1.2

Combine the opposite terms in

z - 8 - z

$z - 8 - z$ .

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Step 4.1.2.1

Subtract

z

$z$ from

z

$z$ .

0 - 8 = 10

$0 - 8 = 10$

Step 4.1.2.2

Subtract

8

$8$ from

0

$0$ .

- 8 = 10

$- 8 = 10$

- 8 = 10

$- 8 = 10$

- 8 = 10

$- 8 = 10$

Step 4.2

Since

- 8 \neq 10

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

No solution

No solution

Step 5

Solve

z - 8 = - (z + 10)

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

z

$z$ .

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Step 5.1

Simplify

- (z + 10)

$- (z + 10)$ .

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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

$10$ .

$z - 8 = - z - 10$

$z - 8 = - z - 10$

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

$z$ .

$2 z - 8 = - 10$

$2 z - 8 = - 10$

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

$8$ .

$2 z = - 2$

$2 z = - 2$

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

$1$ .

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

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

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

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Divide

$- 2$ by

$2$ .

$z = - 1$

$z = - 1$

$z = - 1$

$z = - 1$

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