Pre-Algebra Examples

$2 z - 9 = - 5 - 2 (2 z + 8)$

Step 1

Simplify $- 5 - 2 (2 z + 8)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 z - 9 = - 5 - 2 (2 z) - 2 \cdot 8$

Step 1.1.2

Multiply $2$ by $- 2$ .

$2 z - 9 = - 5 - 4 z - 2 \cdot 8$

Step 1.1.3

Multiply $- 2$ by $8$ .

$2 z - 9 = - 5 - 4 z - 16$

Step 1.2

Subtract $16$ from $- 5$ .

$2 z - 9 = - 4 z - 21$

Step 2

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

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Step 2.1

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

$2 z - 9 + 4 z = - 21$

Step 2.2

Add $2 z$ and $4 z$ .

$6 z - 9 = - 21$

Step 3

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

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Step 3.1

Add $9$ to both sides of the equation.

$6 z = - 21 + 9$

Step 3.2

Add $- 21$ and $9$ .

$6 z = - 12$

Step 4

Divide each term in $6 z = - 12$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 z = - 12$ by $6$ .

$\frac{6 z}{6} = \frac{- 12}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 z}{6} = \frac{- 12}{6}$

Step 4.2.1.2

Divide $z$ by $1$ .

$z = \frac{- 12}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 12$ by $6$ .

$z = - 2$