Algebra Examples

$- \frac{22}{5} z = - \frac{23}{10} (2 z + 1)$

Step 1

Simplify $- \frac{22}{5} z$ .

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Step 1.1

Rewrite.

$0 + 0 - \frac{22}{5} z = - \frac{23}{10} \cdot (2 z + 1)$

Step 1.2

Simplify by adding zeros.

$- \frac{22}{5} z = - \frac{23}{10} \cdot (2 z + 1)$

Step 1.3

Combine $z$ and $\frac{22}{5}$ .

$- \frac{z \cdot 22}{5} = - \frac{23}{10} \cdot (2 z + 1)$

Step 1.4

Move $22$ to the left of $z$ .

$- \frac{22 z}{5} = - \frac{23}{10} \cdot (2 z + 1)$

Step 2

Simplify $- \frac{23}{10} \cdot (2 z + 1)$ .

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Step 2.1

Apply the distributive property.

$- \frac{22 z}{5} = - \frac{23}{10} (2 z) - \frac{23}{10} \cdot 1$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Move the leading negative in $- \frac{23}{10}$ into the numerator.

$- \frac{22 z}{5} = \frac{- 23}{10} (2 z) - \frac{23}{10} \cdot 1$

Step 2.2.2

Factor $2$ out of $10$ .

$- \frac{22 z}{5} = \frac{- 23}{2 (5)} (2 z) - \frac{23}{10} \cdot 1$

Step 2.2.3

Factor $2$ out of $2 z$ .

$- \frac{22 z}{5} = \frac{- 23}{2 (5)} (2 (z)) - \frac{23}{10} \cdot 1$

Step 2.2.4

Cancel the common factor.

$- \frac{22 z}{5} = \frac{- 23}{2 \cdot 5} (2 z) - \frac{23}{10} \cdot 1$

Step 2.2.5

Rewrite the expression.

$- \frac{22 z}{5} = \frac{- 23}{5} z - \frac{23}{10} \cdot 1$

Step 2.3

Combine $\frac{- 23}{5}$ and $z$ .

$- \frac{22 z}{5} = \frac{- 23 z}{5} - \frac{23}{10} \cdot 1$

Step 2.4

Simplify the expression.

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Step 2.4.1

Multiply $- 1$ by $1$ .

$- \frac{22 z}{5} = \frac{- 23 z}{5} - \frac{23}{10}$

Step 2.4.2

Move the negative in front of the fraction.

$- \frac{22 z}{5} = - \frac{23 z}{5} - \frac{23}{10}$

Step 3

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

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Step 3.1

Add $\frac{23 z}{5}$ to both sides of the equation.

$- \frac{22 z}{5} + \frac{23 z}{5} = - \frac{23}{10}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{- 22 z + 23 z}{5} = - \frac{23}{10}$

Step 3.3

Add $- 22 z$ and $23 z$ .

$\frac{z}{5} = - \frac{23}{10}$

Step 4

Multiply both sides of the equation by $5$ .

$5 \frac{z}{5} = 5 (- \frac{23}{10})$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $5$ .

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Step 5.1.1.1

Cancel the common factor.

$5 \frac{z}{5} = 5 (- \frac{23}{10})$

Step 5.1.1.2

Rewrite the expression.

$z = 5 (- \frac{23}{10})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $5 (- \frac{23}{10})$ .

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Step 5.2.1.1

Cancel the common factor of $5$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{23}{10}$ into the numerator.

$z = 5 (\frac{- 23}{10})$

Step 5.2.1.1.2

Factor $5$ out of $10$ .

$z = 5 \frac{- 23}{5 (2)}$

Step 5.2.1.1.3

Cancel the common factor.

$z = 5 \frac{- 23}{5 \cdot 2}$

Step 5.2.1.1.4

Rewrite the expression.

$z = \frac{- 23}{2}$

Step 5.2.1.2

Move the negative in front of the fraction.

$z = - \frac{23}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$z = - \frac{23}{2}$

Decimal Form:

$z = - 11.5$

Mixed Number Form:

$z = - 11 \frac{1}{2}$