Basic Math Examples

$\frac{7}{11} \cdot (z - 4) - \frac{27}{11} = - 5$

Step 1

Simplify $\frac{7}{11} \cdot (z - 4) - \frac{27}{11}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{7}{11} z + \frac{7}{11} \cdot - 4 - \frac{27}{11} = - 5$

Step 1.1.2

Combine $\frac{7}{11}$ and $z$ .

$\frac{7 z}{11} + \frac{7}{11} \cdot - 4 - \frac{27}{11} = - 5$

Step 1.1.3

Multiply $\frac{7}{11} \cdot - 4$ .

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Step 1.1.3.1

Combine $\frac{7}{11}$ and $- 4$ .

$\frac{7 z}{11} + \frac{7 \cdot - 4}{11} - \frac{27}{11} = - 5$

Step 1.1.3.2

Multiply $7$ by $- 4$ .

$\frac{7 z}{11} + \frac{- 28}{11} - \frac{27}{11} = - 5$

Step 1.1.4

Move the negative in front of the fraction.

$\frac{7 z}{11} - \frac{28}{11} - \frac{27}{11} = - 5$

Step 1.2

Combine fractions.

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Step 1.2.1

Combine the numerators over the common denominator.

$\frac{7 z - 28 - 27}{11} = - 5$

Step 1.2.2

Subtract $27$ from $- 28$ .

$\frac{7 z - 55}{11} = - 5$

Step 2

Multiply both sides by $11$ .

$\frac{7 z - 55}{11} \cdot 11 = - 5 \cdot 11$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $11$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{7 z - 55}{11} \cdot 11 = - 5 \cdot 11$

Step 3.1.1.2

Rewrite the expression.

$7 z - 55 = - 5 \cdot 11$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 5$ by $11$ .

$7 z - 55 = - 55$

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 $55$ to both sides of the equation.

$7 z = - 55 + 55$

Step 4.1.2

Add $- 55$ and $55$ .

$7 z = 0$

Step 4.2

Divide each term in $7 z = 0$ by $7$ and simplify.

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Step 4.2.1

Divide each term in $7 z = 0$ by $7$ .

$\frac{7 z}{7} = \frac{0}{7}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $7$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{7 z}{7} = \frac{0}{7}$

Step 4.2.2.1.2

Divide $z$ by $1$ .

$z = \frac{0}{7}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $0$ by $7$ .

$z = 0$