Basic Math Examples

$0 y - 9 z = 4 z$

Step 1

Simplify $0 y - 9 z$ .

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Step 1.1

Multiply $0$ by $y$ .

$0 - 9 z = 4 z$

Step 1.2

Subtract $9 z$ from $0$ .

$- 9 z = 4 z$

Step 2

Divide each term in $- 9 z = 4 z$ by $- 9$ and simplify.

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Step 2.1

Divide each term in $- 9 z = 4 z$ by $- 9$ .

$\frac{- 9 z}{- 9} = \frac{4 z}{- 9}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 9$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 9 z}{- 9} = \frac{4 z}{- 9}$

Step 2.2.1.2

Divide $z$ by $1$ .

$z = \frac{4 z}{- 9}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

$z = - \frac{4 z}{9}$

Step 3

Multiply both sides by $9$ .

$z \cdot 9 = - \frac{4 z}{9} \cdot 9$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Move $9$ to the left of $z$ .

$9 z = - \frac{4 z}{9} \cdot 9$

Step 4.2

Simplify the right side.

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Step 4.2.1

Cancel the common factor of $9$ .

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Step 4.2.1.1

Move the leading negative in $- \frac{4 z}{9}$ into the numerator.

$9 z = \frac{- 4 z}{9} \cdot 9$

Step 4.2.1.2

Cancel the common factor.

$9 z = \frac{- 4 z}{9} \cdot 9$

Step 4.2.1.3

Rewrite the expression.

$9 z = - 4 z$

Step 5

Solve for $z$ .

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Step 5.1

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

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Step 5.1.1

Add $4 z$ to both sides of the equation.

$9 z + 4 z = 0$

Step 5.1.2

Add $9 z$ and $4 z$ .

$13 z = 0$

Step 5.2

Divide each term in $13 z = 0$ by $13$ and simplify.

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Step 5.2.1

Divide each term in $13 z = 0$ by $13$ .

$\frac{13 z}{13} = \frac{0}{13}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $13$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{13 z}{13} = \frac{0}{13}$

Step 5.2.2.1.2

Divide $z$ by $1$ .

$z = \frac{0}{13}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $0$ by $13$ .

$z = 0$

Step 6

The variable $y$ got canceled.

All real numbers

Step 7

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$