Pre-Algebra Examples

$2 (6 - 3 z) - 5 (2 z + 5) = z - 22$

Step 1

Simplify $2 (6 - 3 z) - 5 (2 z + 5)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 \cdot 6 + 2 (- 3 z) - 5 (2 z + 5) = z - 22$

Step 1.1.2

Multiply $2$ by $6$ .

$12 + 2 (- 3 z) - 5 (2 z + 5) = z - 22$

Step 1.1.3

Multiply $- 3$ by $2$ .

$12 - 6 z - 5 (2 z + 5) = z - 22$

Step 1.1.4

Apply the distributive property.

$12 - 6 z - 5 (2 z) - 5 \cdot 5 = z - 22$

Step 1.1.5

Multiply $2$ by $- 5$ .

$12 - 6 z - 10 z - 5 \cdot 5 = z - 22$

Step 1.1.6

Multiply $- 5$ by $5$ .

$12 - 6 z - 10 z - 25 = z - 22$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $25$ from $12$ .

$- 6 z - 10 z - 13 = z - 22$

Step 1.2.2

Subtract $10 z$ from $- 6 z$ .

$- 16 z - 13 = z - 22$

Step 2

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

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Step 2.1

Subtract $z$ from both sides of the equation.

$- 16 z - 13 - z = - 22$

Step 2.2

Subtract $z$ from $- 16 z$ .

$- 17 z - 13 = - 22$

Step 3

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

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Step 3.1

Add $13$ to both sides of the equation.

$- 17 z = - 22 + 13$

Step 3.2

Add $- 22$ and $13$ .

$- 17 z = - 9$

Step 4

Divide each term in $- 17 z = - 9$ by $- 17$ and simplify.

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Step 4.1

Divide each term in $- 17 z = - 9$ by $- 17$ .

$\frac{- 17 z}{- 17} = \frac{- 9}{- 17}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 17$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 17 z}{- 17} = \frac{- 9}{- 17}$

Step 4.2.1.2

Divide $z$ by $1$ .

$z = \frac{- 9}{- 17}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Dividing two negative values results in a positive value.

$z = \frac{9}{17}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$z = \frac{9}{17}$

Decimal Form:

$z = 0.52941176 \dots$