Basic Math Examples

$\frac{4}{5} \cdot (z + 5) + \frac{3}{5} z = 7$

Step 1

Simplify $\frac{4}{5} \cdot (z + 5) + \frac{3}{5} z$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{4}{5} z + \frac{4}{5} \cdot 5 + \frac{3}{5} z = 7$

Step 1.1.2

Combine $\frac{4}{5}$ and $z$ .

$\frac{4 z}{5} + \frac{4}{5} \cdot 5 + \frac{3}{5} z = 7$

Step 1.1.3

Cancel the common factor of $5$ .

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Step 1.1.3.1

Cancel the common factor.

$\frac{4 z}{5} + \frac{4}{5} \cdot 5 + \frac{3}{5} z = 7$

Step 1.1.3.2

Rewrite the expression.

$\frac{4 z}{5} + 4 + \frac{3}{5} z = 7$

Step 1.1.4

Combine $\frac{3}{5}$ and $z$ .

$\frac{4 z}{5} + 4 + \frac{3 z}{5} = 7$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$4 + \frac{4 z + 3 z}{5} = 7$

Step 1.2.2

Add $4 z$ and $3 z$ .

$4 + \frac{7 z}{5} = 7$

Step 2

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

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Step 2.1

Subtract $4$ from both sides of the equation.

$\frac{7 z}{5} = 7 - 4$

Step 2.2

Subtract $4$ from $7$ .

$\frac{7 z}{5} = 3$

Step 3

Multiply both sides of the equation by $\frac{5}{7}$ .

$\frac{5}{7} \cdot \frac{7 z}{5} = \frac{5}{7} \cdot 3$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{5}{7} \cdot \frac{7 z}{5}$ .

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Step 4.1.1.1

Cancel the common factor of $5$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{5}{7} \cdot \frac{7 z}{5} = \frac{5}{7} \cdot 3$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 z) = \frac{5}{7} \cdot 3$

Step 4.1.1.2

Cancel the common factor of $7$ .

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Step 4.1.1.2.1

Factor $7$ out of $7 z$ .

$\frac{1}{7} (7 (z)) = \frac{5}{7} \cdot 3$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 z) = \frac{5}{7} \cdot 3$

Step 4.1.1.2.3

Rewrite the expression.

$z = \frac{5}{7} \cdot 3$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $\frac{5}{7} \cdot 3$ .

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Step 4.2.1.1

Combine $\frac{5}{7}$ and $3$ .

$z = \frac{5 \cdot 3}{7}$

Step 4.2.1.2

Multiply $5$ by $3$ .

$z = \frac{15}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$z = \frac{15}{7}$

Decimal Form:

$z = 2.\overline{142857}$

Mixed Number Form:

$z = 2 \frac{1}{7}$