Basic Math Examples

$\frac{4}{13} \cdot (z - 1) - \frac{74}{13} = - 6$

Step 1

Simplify $\frac{4}{13} \cdot (z - 1) - \frac{74}{13}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{4}{13} z + \frac{4}{13} \cdot - 1 - \frac{74}{13} = - 6$

Step 1.1.2

Combine $\frac{4}{13}$ and $z$ .

$\frac{4 z}{13} + \frac{4}{13} \cdot - 1 - \frac{74}{13} = - 6$

Step 1.1.3

Multiply $\frac{4}{13} \cdot - 1$ .

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Step 1.1.3.1

Combine $\frac{4}{13}$ and $- 1$ .

$\frac{4 z}{13} + \frac{4 \cdot - 1}{13} - \frac{74}{13} = - 6$

Step 1.1.3.2

Multiply $4$ by $- 1$ .

$\frac{4 z}{13} + \frac{- 4}{13} - \frac{74}{13} = - 6$

Step 1.1.4

Move the negative in front of the fraction.

$\frac{4 z}{13} - \frac{4}{13} - \frac{74}{13} = - 6$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$\frac{4 z - 4 - 74}{13} = - 6$

Step 1.2.2

Subtract $74$ from $- 4$ .

$\frac{4 z - 78}{13} = - 6$

Step 1.2.3

Factor $2$ out of $4 z - 78$ .

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Step 1.2.3.1

Factor $2$ out of $4 z$ .

$\frac{2 (2 z) - 78}{13} = - 6$

Step 1.2.3.2

Factor $2$ out of $- 78$ .

$\frac{2 (2 z) + 2 (- 39)}{13} = - 6$

Step 1.2.3.3

Factor $2$ out of $2 (2 z) + 2 (- 39)$ .

$\frac{2 (2 z - 39)}{13} = - 6$

Step 2

Multiply both sides by $13$ .

$\frac{2 (2 z - 39)}{13} \cdot 13 = - 6 \cdot 13$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{2 (2 z - 39)}{13} \cdot 13$ .

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Step 3.1.1.1

Cancel the common factor of $13$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{2 (2 z - 39)}{13} \cdot 13 = - 6 \cdot 13$

Step 3.1.1.1.2

Rewrite the expression.

$2 (2 z - 39) = - 6 \cdot 13$

Step 3.1.1.2

Apply the distributive property.

$2 (2 z) + 2 \cdot - 39 = - 6 \cdot 13$

Step 3.1.1.3

Multiply.

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Step 3.1.1.3.1

Multiply $2$ by $2$ .

$4 z + 2 \cdot - 39 = - 6 \cdot 13$

Step 3.1.1.3.2

Multiply $2$ by $- 39$ .

$4 z - 78 = - 6 \cdot 13$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 6$ by $13$ .

$4 z - 78 = - 78$

Step 4

Solve for $z$ .

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Step 4.1

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

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Step 4.1.1

Add $78$ to both sides of the equation.

$4 z = - 78 + 78$

Step 4.1.2

Add $- 78$ and $78$ .

$4 z = 0$

Step 4.2

Divide each term in $4 z = 0$ by $4$ and simplify.

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Step 4.2.1

Divide each term in $4 z = 0$ by $4$ .

$\frac{4 z}{4} = \frac{0}{4}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $4$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{4 z}{4} = \frac{0}{4}$

Step 4.2.2.1.2

Divide $z$ by $1$ .

$z = \frac{0}{4}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $0$ by $4$ .

$z = 0$